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SMITE - A SECOND ORDER EULERIAN CODE FOR HYDRODYNAMIC AND ELASTIC-PLASTIC PROBLEMS

Samuel Z. Burstein, et al

Mathematical Applications Group, Incorporated

Prepared for:

Ballistic Research Laboratories

August 1975

DISTRIBI,TED BY:

mi] National Technical Information Service U. S. DEPARTMENT OF COMMERCE

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CONTRACT REPCRi NO. 255

SMITE - A SECOND ORDER EULERIAN CODE FOR

HYDRODYNAMIC AND ELASTIC-PLASTIC PROBLEMS

Prepared by

Mathematical Applications Group, Inc. 3 Westchester Plaza Elmsford, New York 10523

D D C ^Uil^

August 1975

Approved for public rcleise; distribution unlimited.

Copy ovc;;;--. .. . uoc-s noi gensit fully logibb reproduction

USA BALLISTIC RESEARCH LABORATORIES ABERDEEN PROVING GROUND, MARYLAND

B«p(jdu<«d by

NATIONAL TECHNICAL INFORMATION SERVICE

US D«pirtment ol CommMcm Spnnotnld, VA 23IS1

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Destroy this report when it is no longer needed. Do not return it to the originator.

Secondary distribution of this report by originating or sponsoring activity is prohibited.

Additional copies of this report may be obtained from the National Technical Information Service, II.S, Department of Commerce, Springfield, Virginia <;21S1.

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The findings in this report are not to be construed as an official Department of the Army position, unless so designated by other authorized documents.

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1 REPORT DOCUMENTATION PAGE READ mSTRUCTIONS BEPORE COMPLETINO FORM

11. RCPOAT NUMBCR

BRL CONTRACT REPORT NO. 255 i. OOVT ACCCUMM NO >. RECIPIENT'S CATALOG NUMBER

1«. TITLE f«n«Ju»l(II.)

ISMITE A Second Order Eulerian Code for lllydrodynaraic and Elastic-Plastic Problems

S TYPE dt REPORT t PERIOD COVERED

Final ». PERFORMING ORQ. REPORT NUMBER

h. AUTHOR^

jSamuel Z. Burstein lllarold S. Schechter IF.. L. Türkei

t. CONTRACT OR GRANT NUMBERCaj

DAAD05-:j-C-0512

1» PERFORMINO ORGANIZATION NAME AND AODRcis jMathematical Applications Group, Inc. 13 Westchester Plaza IFlmsford, New York 10523

10. PROGRAM ELEMENT, PROJECT, TASK AREA t WORK UNIT NUMBERS

1T662618AH80

1" CONTROLLING OFriCS NAME AND ADDRESS

IIISA Ballistic Research Laboratories iTerminal Ballistics Laboratory jAberdeen Proving Ground, MD 21005

11. REPORT DATS

August 197S 1«. NUMBER OF PAGES

162 1 14. MONITORING AGENCY NAME • ADORESV" dlllttmil (ran Conlrallln« O.'Uc«) IB. SECURITY CLASS, (ol «il» rapori;

UNCLASSIFIED ISa. OECLASSIFICATION/DOWNOR«OING

SCHEDULE

1 M. DISTRIBUTION STATEMENT (al tftta Naporl)

| Approved for public release: distribution unlimited.

1 17. DISTRIBUTION STATEMENT (ol Ihm •»•Iracl mltrmd In Block 10, II dllltrmnl Iron Ktporl)

I II. SUPPLEMENTARY NOTES 1

1 19. KEY WORDS (Contlnum on rmvmtao old* 11 nacaaaary and Idmnttly by block numbarj

iBallistic Impact Hydrodynamic | IPenetration Elastic-Plastic Code 1 iFinite Difference 1 Second Order Numerical Methods 1

JHulerian Code j 1 20. ABSTRACT (Contlnum an rmvmmo «Ida If nacaaaarr and Idontllf br block number)

A computer code for hydrodynamic and elastic-perfectly plastic problems is 1 described. The model uses a second order finite difference method based upon 1 a Eulerian formulation of the basic differential equations. The algorithm j utilizes an individual grid for each material domain, determined by j Lagrangian type boundary points which are subject to free surface and inter- 1 face conditions. The only communication between domains is through their j common interfaces. |

MFORM I JAN 71 1473 EtMTIOM OF I NOV »t IS OBSOLETE UNCLASSIFIED

SECURITY CLASSIFICATION OF THIS PACE f»t>an Data EmaradJ

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TABLE OF CONTENTS

I. INTRODUCTION .,..,... 5

II., SUBROUTINE LOGIC. 6

2.1 Main Program .......... 6

2.2 ADJINT .......... 6

2.3 BONDRY .......... 7

2.4 BPOSN. . 8

2.5 BVALU 8

2.6 DENSE, 8

2.7 FDIFF. ... ........... 9

2.8 FINISH 10

2.9 GENVAL . . . 10

2.10 INFACE ..... ........... 10

2.11 INITAL . 11

2.12 INTRPL 11 2.13 IPOSN. 13 2.14 MVBND„ ....................... 13 2.15 ONESTP ....................... 13 2.16 OUTPUT 15 2.17 PLTOUT .... o .................. 15 2.18 PRNPLT ....................... 15 2.19 PRS. ...... ............ 15 2.20 RELABL ............... ........ 15 2.21 SAVE ............ ....... 16

III. GENERAL PROGRAM DESCRIPTION 17

3.1 Flow Chart ....... 3.2 Subroutine References. , 3.3 Common Block References. 3.4 Storaye Arrangement. . . 3.5 Major Variables. . . . .

o o o • 17 18 19 20 21

IV. PROGRAM USAGE e o o 30

4.1 4.2 4.3 4.4

Input. . , , . Sample Input , Diagnostics. . Sample Output.

30 35 48 49

PROGRAM LISTING . o • o e • 91

DISTRIBUTION LIST 162

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I. INTRODOCTXON

This manual describes the SMITE (Second order Moving Interface Two dimensional Eulerlan) code for hydrodynamic and elastlc-perfectly plastic problems. The code is based on an I ilerlan formulation for the numerical model. Eulerlan methods are characterized by a mesh which la fixed in space for all times. The materials are allowed to move freely through this grid. In the SMITE code, each material has its own Independent grid. Thus, the mesh spacing and number of mesh grids in one material is in no way affected by that in another material. The equations are also solved in a trans- formed plane. This allows for transformations to be used which concentrate the mesh points in regions of greatest Interest.

The extent of each domain is determined by particles or material points which define the domain boundary. These points are moved in a Lagrangian sense by integrating the ordinary differential equations relating their positions and velocities. The values at the boundary points are subject to free surface and interface conditions. The interface conditions provide the only communication butweon the various material domains.

The model upon which the SHITE code is based is fully described in the report "A Second Order Numerical Model for High Velocity Impact Phenomena" by the same authors. All references in this manual are to sections of the above report.

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II. SUBRDOTiy; LOGIC

2.1 Main Program

The main program controls th« overall logical flow of the code. INITAL is called to read input and initialise the run. All tine increments are added to the starting time to determine when the processes dependent on these Increments will next occur. The cycle count is incremented to start the main loop.. The time step is set to the minimum of the CFL time step determined for all materials. If this time step is lass than the minimum allowed, a message is printed and the run aborted. The time is incremented and MVBND called to move all material boundaries. ADJINT is then called to determine the new inter- face locations and adjust the boundary positions accordingly. Initial boundary values for each material are extrapolated fron the interior by calling BOtJDRY DENSB Is then called to satisfy boundary conditions- The routine now loops through the material. GENVAL sets the proper material dependent mesh and array bound values. FDIFF Is called next to solve the finite difference equations. FINISH is then called to determine if any shifting of the domain or rezoning of its boundary is necessary. The positions where the boundaries cross the mesh lines are determined by calling BPOSN and BVALU is called to calculate the crossing coordinates and the variable values at these crossing points. Values are then interpolated at all interior mesh points for which the finite difference equations could not be used by calling INTRPL. This ends the material loop. The error fla<j is checked and If it is set the run is aborted SECOND is called to obtain the elapsed running time. If the running time or problem time are greater than their maximum values, the run is ended. The problem time is compared to the time at which the next printer plot is desired. If this time has been exceeded PRNPLT is called and the printer plot increment is added to the printer plot time. The same is done with PLTOÜT for plotter output, OUTPUT for printed output and SAVE for restart output. The next time cycle Is then started. At the end of a run all desired output is generated regardless of the respective time increments,

2.2 ADJINT

Subroutine ADJINT determines the locations of material interfaces and adjusts boundary positions accordingly. In its present state, it is a rather ad hoc routine which makes strong assumptions regarding material orientation and relative position. If a particular problem does not meat these conditions, ADJINT will have to be modified or rewritten for that problem. It is assumed that all interfaces exist at the start of the problem. If the boundaries of the two materials penetrate each other, it is assumed that tho first material (material A) that appears in the interface specification is the predominant material. The interface points of the second material (material B) will be re- placed by those of material A. The task of ADJINT is to determine the exact extent of the interface. All boundaries consist of three segments which are divided by the boundary points into linear sub-segments. It is assumed that the interface starts with the first point of material A and the last point of material B and hence that material A is on the right of material B. In order to find the end of the interface, the logic is to find a point on each boundary not on the interface and then trace the boundaries toward the interface until they first intersect. It is further assumed that the interface lies entirely within the third segment of material B. The maximum z coordinate of material B

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Is found and then the last point of material A whose z .-oordlnate Is less than this maximum value. The next point on material A Is the endpolnt of the last material A sub-segment that can Intersect the aoundary of material B so that no additional points on the material A boundary are considered. The maximum r coordinate of the valid material A points in determined and then the first material B point less than this value. This point defines the endpolnt of the first material B sub-segment than can Intersect the boundary of material A. A box is drawn around the material B sub-segment and the first and last material A sub-segments that enter this box are de- termined. Only those sub-segments of material A between these end segments can possibly intersect the sub-segment of material B. Starting with the last material A sub-segment, each sub-segment is tested for an intersection. If an intersection is found then the lower sub-segment endpolnts define the end of the respective Interface segments. If an intersection is not found, a box is drawn around the next material B sub-segment and the search continues. Once an intersection is found, the material B interface segment is replaced by the material A interface segment. Since this replaceaient may add to the total number of material B boundary points a test is made to see if the number of points on the material B boundary exceeds the maximum allowable. If so, a message is printed and a flag is set to Abort the run at the end of the cycle.

If material B represents material domain 3 special logic is provided., In this case, the interface segments as defined upon entering ADJINT are used. The points of the material B segment are simply replaced by the points of the material A segment. No assumptions are made about the segment location or boundary orientations,

2.3 BONDRY

This subroutine obtains values for all variables on the boundaries of the material domains. The boundary point coordinates, which upon entering BONDRY are in z-r space, are first transformed to a-H space. The arc length along the boundary at each point is then computed. Boundary values are extrapolated from the interior by choosing the closest interior mesh point to a boundary point and assigning the dependent variable values at this mesh point to the boundary point (5.a). The four mesh points surrounding a boundary point are examined» If the closest mesh point is interior to the domain it is chosen; if it is not interior, the next closest is selected, etc. If none of the four points are interior to the domain, the boundary point retains the values associated with it from the previous time step. These extrapolated values are then smoothed to prevent a step function appearance. The smoothing formula used is

b. =a. + -r r (a.^, -2a. +a. ,) i i 4 i+l i i-l

where r is the ratio of the time step used to the time step calculated for the material. This ratio prevents the smoothing operation from propagating signals through a material at a rate greater than the CPL stability condition would allow.

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2.4 E?OSN

The positions where the boundaries cross the mesh lines are determined by subroutine BPOSN. Two similar arrays are dsflned, one for the mesh lines in each coordinate direction. Thase arrays are computed by systematically following the boundary. The logic for both sets Is identical, so that only the computation of the crossings of the lines 2=constant will be described . Let Int(a) be the largest integer less than or equal to a and Az be the mesh spacing. Then i=lnt(2 /&z) implies that the boundary point p with axial

m m coordinate z lies between mesh lines 1 and 1+1. Starting with n=Int(2./Az)

values of i are determined for succeeding boundary points until i is not equal to n. If 1 is less than n, mesh line n has been crossed; if 1 is greater than n, mesh line n+1 has been crossed. Let p ^ be the boundary point where i

m+1 changed value. Then the boundary crossed a mesh line between point m and m+1 The integer m is entered into the array for the mesh line that was crossed and all entries for that mesh line are ordered according to increasing radial coordinate values. A total of |n-l| mesh lines may have benn crossed and an entry is mada for each of them. The Integer n is then reset to n=Int(z .,/Az) and the procedure continues until the entire boundary has been traced

2.5 BVALU

BVALU determines the coordinates of the points where the boundaries cross mesh lines and the values of the dependent variables at these points. The co- ordinates of a crossing are defined as the intersection of a mesh line with the straight line segment between the boundary points on either side of it The dependent variable values are then obtained by interpolating along this line segment.

2.6 DEHSB

Boundary conditions are satisfied by subroutine DENSE INFACE is called to satisfy conditions on all interfaces. All non-interface, i.e free surface, points are then determined. The normal stress at these points is then set to zero (5.b) .

All interfaces are examined and an array is created which specifies, for each material, the first and last points of all boundary segments that are interfaces. These segment endpoints are arranged in ascending order with a zero after the last endpoint to signal the end of the array. Each material is then processed. The boundary coordinates are transformed from a-ß to z-r space and the transformed values are stored in a temporary array. Each free surface segment, if any, will be all those boundary points lying between the high end- point of one interface segment and the low endpoint of the next interface seg- ment The local slope at a point (z.,r.) is obtained from tan ^ = (e -z. )/ (r. ,-r, .), For the normal stress to vanish, we must have 1~

i+l i-l 2 2 p = S sin 'ii + 2 Z sin ij* cos ty + S cos ty

This condition on pressure is satisfied by finding the internal energy and using Newton-Raphson iteration to solve the equation of state for the proper density,. The d:nsit'/ at the free surface boundary point is then set to this value, If the iterition does not converge, a message is printed and a flag is set to abort the run at the end of the cycle

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2.7 FDIFF

The finite difference equations at interior mesh points are evaluated in subroutine FDIFF (4.a). The entire mesh is shifted in memory two radial lines to the right (toward higher index of the axial mesh). It should b« noted that the solution at any mesh point depends only on the mesh lines through that point and on either side of it. Hence, if the solution proceeds along radial mesh lines and the answers are stored back two lines to the left, only room for two additional mesh lines need be added to the memory arrays to allow the old solution to be overwritten by the new solution. The eight nearest neighbors of a mesh point are examined to determine if any lie outside the domain. The neighbors are ordered and if the nth neighbor is missing 2n is added to a code word. The neighbors are ordered counterclockwise with the four nearest neighbors first starting with the right and then the four outer neighbors start- ing with the upper-right. If the code used is non zero, all neighbors are not interior to the domain and ONESTP is called. If all neighbors are present, the two

3 L

7 ' 1 B

step solution may be used.

At each mesh point in the nine point solution lattice, the transformed seven component vector w and its vector functions f, g and h are computed and stored in 3x3 matrices. In both steps of the two step method, the difference equations for the first four components of w are evaluated first and then the difference equations for the three stress components are evaluated. Predicted values at the four midpoints oi the boxes shown in the above figure are obtained. That portion of the second step which depends on values at time t is also ob- tained. The artificial viscosity is included in the partial second step eval- uation.

The predicted values are used to define the f, g and h vectors at the lattice midpoint. The remainder of the second step of the solution that de- pends on the predicted values is then obtained. This solution is transfoimed back to its non-conservative form and stored in the solution array. A test is then made to determine if the stress components satisfy the yield condition, If they do not satisfy the yield criteria the stresses are modified to force them back on to the yield surface (3„b) . Finally, the CFL stability parameter at the mesh point i« evaluated. If the solution appears to be going unstable, ONESTP is called in an attempt to obtain a more stable value. After all mesh points have bet-n evaluated, the L array is shifted back to it original locations The CFL stable stepsize for the material is then computed.

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2.8 FIMISH

This subroutine checks the position rf each domain relative to storage and of the boundary points of a domain relative to each other. As a domain moves through its mesh it may cover sauie mesh points and uncover others. The algorithm requires at leaut one line of exterior mesh points in all dir- ections at the start of a tine step. This ensures the existence of mesh points to allow the domain to expand in any direction. The boundary is checked to see if any point on it has exceeded the mesh. If the mesh 13 ex- ceeded in one direction, the opposite direction is checked. If the opposite direction has more than two exterior mesh lines, the domain is shifted as far as possible in that direction. This is done by shifting nil interior arrays in storage and performing a linear translation on the proper a-6 coordinate., If a shift is not possible, a flag is set to abort the run at the end of the cycle. A message is printed together with the domain limits and the boundary coordinates in a-6 space.

The arc length of each boundary segment is compared with the length of that segment when it first contained its present number of points. If the arc length more than doubled, the number of points is Increased by fifty percent. All boundary points above the segment are shifted up to make room for the additional points. Tracer point and interface endpoint information that refers to the shifted boundary points is also adjusted. If the arcsize has not doubled the segment is also checked for relative distance between adjacent points. If the deviation from the average is too large the points in the segment are redistri- buted. The actual redistribution of points, whether the total number remain the same or has been Increased, is performed by subroutine RELABL,

2.9 GENVM,

Values of various variables that depend on material properties and mesh geometry and which vary from one material domain to the next are sot by sub- routine GENVAL.

2.10 INFACE

The boundary conditions on interfaces are satisfied by subroutine INFACE, These conditions are the continuity of normal velocity and stress (5,0,) „ The local slope at ä point (z.,r.) is obtained from tan ij; = (z. -z. )/(r. -r. ,) ,

The boundary values obtained from the interior on each side of the interface are used to calculate a normal and tangential velocity and a normal stress, A weighted average of the normal velocities and another weighted average of the normal stresses are used to define a common normal velocity and a common normal stress. The common normal velocity together with the previously calcu- lated tangential velocities on both sides of the- interface are used to obtain the adjusted axial and radial velocities. The common normal stress provides a condition for pressure on both sides of the interface. Fixing the internal energy, a Newton-Raphson iteration is used to solve the equation of state for the proper density. If the iteration does not converge a message is printed and a flag is set to abort the run at the end of the cycle.

10

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2.11 1NITAL

All input data Is read In subroutin« INITAL. General run parameters are read first and the interfaces are defined. If the run is a continuation of a previous run, the interface parmeters are overwritten by those on the restart tape. Input is then read for each material domain in turn. The domains are numbered according to the order in which they are input. The bounds of the array segments associated with the material are calculated and these segments are then zeroed out. Non-dinensionalization factor.» are then generated. Length is non-dimensionalized by mesh size so that the mesh size is unity. The scaling factor used for time is set to that for length so that velocity is non-dimensionalized by a cpeed of unity; hence non-dimensional velocity numerically remains the sane as dimensional velocity. The initial material density is used to non-dimensionalizc density« The constants needed in the coordinate transformations are calculated and the input boundary coordin- ates are transformed to a-ß space. The transformed mesh size is unity for both coordinates so that the arc length of a boundary segment is an approximate measure of the number of mesh segments it traverses. Thus setting the number of points in each boundary segment to twice its arc length will result in approximately two boundary points per mesh segment. Values of r and its deri- vatives are calculated for each radial mesh point and mid-point,, RELABT, is called to generate the proper number of equally spaced boundary points from the input values. These points are then set to their initial values» The points where the boundary crossed the mesh lines and values at these points are de- termined by calling BPOSN and BVALU. The interior points are set to their initial values and IPOSN is called to determine which points are interior and which exterior to the domain. A line of reflected points below the axis of symmetry is then set. The CFL stepsize for the material is calculated as is the initial arc length of each boundary segment. If this run is a continuation of a previous run, the initial values are read from the rescart tape. The restart domain is then shifted to the positions required by the first axial and radial mesh point interior to the domain as specified by the input. For a restarted problem thore portions of INITAL that initialize domain values are skipped. After all materials have been input and initialized the time incre- ments for the various types of output are examined. If the increment is nega- tive it is set to a large number so that it will never be reached and its corresponding type of output will never occur. Otherwise the associated output subroutine is called to output the initial data.

2.12 INTRPL

The solution at mesh points that were too near to the domain boundary, that have just become interior to the domain or where the finite difference solution appeared to be going unstable is evaluated by interpolation from neighboring interior and boundary crossing points in subroutine INTRPL. First subroutine IPOSN is called to determine which points are interior to the domain. An axial mesh line below the axis of symmetry is reflected from the mesh line above the axis of symmetry. The mesh is then swept to determine which points remain to be computed by interpolation. Linear interpolation from adjacent interior or boundary crossing points is used. The four nearest neighbors to the mesh point are examined. Each may be a boundary crossing point, an in- terior point that was obtained from the finite difference equations or an in-

11

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terlor point that must be Int-jrpolatad. These three posalbllltles at the four neighbors represent 81 possible configurations. Each configuration Is accounted for and a point on either side '. the mesh point Is selected, If possible, for the Interpolation process. Pol ts that themselves must be Interpolated are not selected since they may not as yet have bean evaluated. After the entire mesh has been swept the points that ware Interpolated are redefined a* normal Interior points. A line of reflected values la again generated below the axis of synnecry to .account for any recently Interpolated values. The 81 possible configurations are represented by the codes In the following table. A 0 represents a boundary crossing point« a 1 represents an Interior point that was obtained from the finite difference equations and a 2 represents an Interior point that must be Interpolated. Reading the numbers from right to left, the digits represent the point below, above, to the left and to the right of the mesh point. The points that were selected ioz use in the interpolation are underlined. In scune cases only one point wa •• used. Here the interpolated values were set directly to the values at that pcin .

1. 0000 22. 0210 42. 1112 62. 2021_

2. 0001 23. 0211 43. 1120 63. 2022

3. 0002 24. 0212 44. 1121 64. 2100

4. 0010 25. 0^20 45. 1122 65, 2101

5. 0011 26. 0221 46. 1200 66. 2102

6. 0012 27. 0222 47. 1201 67. 2110

7. 0020 28. 1000 48. 1202 68. 2111

8. 0021 29. 1001 49. 1210 69. 211 2

9. 0022 30. 1002 50. 1211 70. 2120

10. 0100 31. 1010 51. 1212 71. 2121

11. 0101 32, 1011 52. 1220 72. 2122

12,. 0102 33. 1012 53. 1221 73. 2200

13. 0110 34. 1020 54. 1222 74. 2201

14. 0111 35. 1021 55, 2000 75. 2202

15. 0112 36. 1022 56. 2001 76. 2210

16. 0120 37. 1100 57. 2002 77. 2211

17. 0121 38. 1101 58. 2010 78. 2212

18. 0122 39. 1101 59. 2011 79. ?220

191 0200 ■lO. 111C bL , J012 Pf'. ?221_

20. 0201 41. 1111 61. 2020 81. 2222

21. 0202

12

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2.13 IPOSN

The L array, which spcclfle* whether a mesh point is In a domain or not, is set in subroutine IPOSN. The crossing points of the boundary with the mesh lines are used to determine what is exterior and what is interior to the domain. The mesh is first swept along the lines r - constant. All mesh points along such a line up to the first boundary crossing are outside the domain. All points fron the first crossing to the second crossing are inside. The next set of points are outside, then inside, etc. If a point is outside the domain, L is set to 0. If a mesh point is inside and L has been set to 2 because the point could not be calculated from the finite difference equations, it remains set at 2. Otherwise L is set to 2-L. Thus for all exterior points L Is 0, for all interior points that were calculated fron the finite difference equations L is 1 and for all interior points that have not yet been calculated L is 2. Interpolation errors in obtaining the boundary crossings may cause a mesh point to appear interior when one coordinate direction is considered, yet exterior when the other coordinate direction is considered. The algorithms require a mesh point to be interior no matter which coordinate direction is considered. To allow for this the boundary crossings of the mesh lines z ■ constant are also considered. The crossings are followed as before except that only exterior points need be considered. L is set to 0 for these points so that L will be non zero only for those mesh points which appear interior no matter which way the mesh is swept. For the z « constant mesh crossings the assumption that all mesh points until the first crossing are exterior is valid only if the lines are swept from above the domain toward the axis of symmetry.

2.14 MVBND

In this subroutine the domain boundaries are moved in time by using a simple Euler integration (5.a). The coordinates of the boundary points are trans- formed from o-B space to z-r space and the velocities are integrated with res- pect to time to find the new boundary positions. These new positions are then in the z-r coordinate system.

2.15 ONESTP

The one step finite difference equations for mesh points whose nine point solution stencil does not lie entirely in the domain are evaluated in subroutine ONESTP (4.b). As described in FDIFF, a code word is generated to specify which neighbors of the mesh point are missing. If this word is divided by 16 the result v/ill refer to the four outer neighbors while the remainder refers to the four nearest neighbors. First derivatives and non mixed second derivatives may ba approximated to second order by using the two points on either side of the mesh point in the required direction. These two points will be either mesh points or boundary crossing points. The four outer neighbors are required only for approximating the second mixed partial derivatives. Each of there outer points may be represented by a Taylor's series about the central mes i po'nt. Combinations of these series will yield formulas for the mixed derivative in terms of the outer points and the first and non mixed second derivatives De- pending upon the combinations used, these formulas may be first oz second order accurate. However, first order accuracy in the second space derivatives is all that is required for the overall difference scheme to remain second order accurate. By thus splitting the four outer neighbors from the four nearest neighbors the 256 possible combinations of missing points may be dealt with by first considering the 16 possibilities relating to the four nearest neighbors and then the 16 possibilities relating to the four outer neighbors.

13

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The derivatives are evaluated firat in the axial and then In the radial direction. In either case there are four posaibilitiea to consider. There may bo neah points on both aides, a mesh point on either side and a boundary crossing on the opposite side or boundary crossings on both sides. When there Is a boundary croaeing, the distance to the boundary is calculated. If this distance is less than the allowable diatance the point is skipped to be later evaluated by interpolation in subroutine INTRPL. After the derivatives in each direction are obtained the nixed derivatives are r-valuated. These space derivatives are combined into the expressions appear 1.1 in the one step equations and these equations are computed. The artificial viscosity is then added. A test is made to determine if the stress components satisfy the yield condition. If they do not satisfy the yield criteria the stresses are modified to force them back onto the yield surface (3.b). Finally, the CFL stability parameter at the mesh point is evaluated. If the solution appears -to be going unstable it is discarded to be later evaluated by interpolation in subroutine INTRPL.

The following table will illustrate the code used for missing points.

Code

1. 0000

2. 0001

3. 0010

4, 0011

5. 0100

6. 0101

7. 0110

8. 0111

9. 1000

10. 1001

11, 1010

12. 1011

13. 1100

14. 1101

15. 1110

16. 1111

Date Used for Derivative Approximation

use all points

use lower right and lower left

use lower right and upper right

use lower right and lower left

use uppe~ left and upper right

use lower right and upper left

use lower right and upper right

use lower right

use lower left and upper left

use lower left and upper left

use lower left and upper right

use lower left

use upper left and upper right

use upper left

use upper right

skip and interpolate

A 0 represents the presence of a point while a 1 means it is outside of the do- main. The codes may represent the ordering of the 16 possibilities for both the four nearest neighbors and the four outer neighbors. Reading from right to left the digits represent, for the nearest neighbors, the points to the right, above, left and below. For the four outer neighbors the order is upper right, upper left, lower left and lower right. In representing the outer neighbors the codes are followed by an indication of which of the points are used in eval- uating the mixed derivatives.

14

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2.16 OUTPUT

This routine prepares all printed output. All output is of dimensioned variables and in z-r space. The output proceeds according to material domains. The boundary points appear first. If both 1PRINT and JPRINT are not zero, the Interior mesh points appear next. They are numbered along axial lines with the line nearest to the axis of synmetry first. Only those interior points which are also interior to a box of size IPRINT tines JPRINT are printed. This box starts at the left boundary if IFRINT is positive or ends at the right boundary if IPRINT is negative. It starts at the bottom boundary if JPRINT is positive or ends at the top boundary is JPRINT is negative. The tracer particles are output next. Their values are obtained by interpolation from the proper boundary points. After all domains have been printed the boundary points that are interfaces are identified.

2.17 PLTOUT

Information is prepared in PLTOUT for processing by separate plot programs. The z-r space boundary coordinates, the tracer particle coordinates and the tracer particle velocities are calculated and then written out. All mesh points which are in a plastic region are then obtained. The coordinates of these points are then written out in blocks of 100 points.

2.18 PRNPLT

This subroutine prepares printer plots of the domain boundaries. The boundary points are transformed to z-r space and then scaled to inches of plot. The printer plot routine PRNT is then called for each point to plot the arrays.

2.19 PRS

PRS is a function subroutine to evaluate the equation of state. If the logical variable PDER is true it must also evaluate the partial derivatives of pressure with respect to density and internal energy. The routine supplied uses the Tillotson equation of state but may be replaced by any user written routine.

2.20 REXABL

The points defining a boundary segment eure redistributed over that segment in subroutine RE1ABL. The positions of tracer particles and interface end points are also redefined in relation to the new boundary poir .s. The point coordinates and function values are considered to be functions of arc length along the boundary. The total arc length is divided into evenly spaced intervals by the number of points in the new net. At the end points of the evenly spaced intervals, new point coordinates and function values are interpolated from the old coordinates and values. The arc length value at a tracer particle is also used to find the exact new interval in which that particle lies and its relative position in that interval is then calculated. The new boundary points which define interface endpolnts will be those points bounding the largest segment wholly contained in the old interface segment.

15

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2.21 SAVE

Information needed to continue the calculation in a aubeequent run is output by subroutine SAVE. Before being output, all dooains are shifted as far to the left and bottom as possible. Only those aesh points interior to the smallest mesh rectangle containing the domain are than output. This allows for the possibility of the restarted problem being run using smaller arrays and less computer memory.

16

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III. GENEHM. PROGWM DESCRIPTION

3.1 Flow Chart

Read Input and

Initialize

Clean Up and Stop

Yes

Determine Time Step

Start Material Loop

Solve for Interior Points

A Ves

No

Move all Boundaries

Produce Printer

Plots

Adjust Values for Boundary Conditions

Shift and Rezone if Required

Interpolate Interior Points Not Yet Found

Write Restart Data on Tape

Determine Interfaces

Obtain Boundary Values

Determine Positions of Boundary Crossings

Interpolate [Values at Boundary

[rrossinos

.Yes

Write Plot Data on

Tape

No 'Printer ^ {>.

atput?^

Produce Printed

Output

17

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3.4 Storag» Arrangement

The number of neah point» In each coordinate direction and the number of boundary points may vary from run to run and from material to material. In order to efficiently utilise coaputer memory the storage arrays have no fixed dimensions for these quantities. All materials are stored consecutively. The area reserved for each material is ccnputad fron input parameters. The index of any point in a material is computed relative to a reference value for that material. If KS is the reference value for a material then the point in that material with index K would be referred to in the array with index KS+K. The axial arrays are those in ooonon BNDCRS whost name contains T. and their reference is IS. The radial arrays are those in oomncn BNDCRS whose name contains J and all arrays in coimnon MSHFCN. The radial reference is JS. The first dimension of these arrays controls the maximum number of points for all materials and the second dimension controls the maximum nvanber of boundary crossings in these directions. Thus, if IMAX and JMAX are the axial and radial dimensions, respect- ively, and for each material the maximum number of axial points is NI and the maximum number of radial points is NJ, then the requirement is

lm < IMAX MNJ+1) < JMAX

where the summation is over all materials. The addition of 1 to the NJ is to take account of the reflected line of lata points below the axis of »ynmetry. The arrays for interior mesh points are in blank conoon and have reference US. A mesh point of axial index I and radial index J is referred to in the arrays with the single index US + (J-l) (NI+2) + I. If the array dimension is UMAX then the requirement on the materials la

S(NI+2) (NJ+1) <_ UMAX

The 2 that is added to NI allows for shifting as stated in the description of subroutine FDIFF. The boundary arrays are in common BUDVAL and have reference IBS. For dimensions BMAX and maximum per material of NB the storage require- ment is again

INE < BMAX

Temporary arrays for boundary points that are used separately for each material are in common SCRTCH. The storage requirement here is just that the maximum number of boundary points for any material be less than the array dimension. The maximum number of materials is the first dimension of the arrays in common ZONES, the second dimension in MATARR, the first dimension in TRCPRT and the second dimensions of the array NONIN in comnon INTFC. The maximum number of tracer particles per material is the second dimension of the arrays in common TRCPRT. The maximum number of interfaces is controlled by the array INFC in common INTFC which has six entries per Interface while the maximum number of interfaces one material may have with all other materials is controlled by the first dimension of NONIN. NONIN must have storage for two entries per Interface plus one additional entry to signal the last interface for the material.

20

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IV. PROGRMt USAGE

4.1 Input

There are three types of input data» Integer (I), real (R) and alpha-

numeric (A). An integer is a number without a decimal point which must be

right justified in its field. A real number has a decimal point which may be

followed by an exponent of the form E+N. The +N represents the power of 10 by

which the number is to be multiplied. The + may be omitted if N is positive

and the E need not appear if either the + or - is present. If an exponent is

present it must be right justified in the field. Alphanumeric input consists of

exactly the punched characters and blanks appearing in the field. A description

of the necessary input data for SMITE follows. The card number refers to the

type of input. If more than one card is necessary for this input, there may be

several cards of the same type number. A number in parenthesis indicates an

optional card.

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4.2 Sample Input

Complete listings of the input decks for the two Silver Bullet compu- tations (without and with a sheath) (6.0) appear on the following pages. In addition, listings of sample input decks for the following five geometric and material combinations are given. These five cases have not actually been run. They are presented only as Illustrations of various possible input con- figurations.

Case 1. A blunt truncated mild steel rod (1020) impacting a 0.635 cm (1/4") aluminum target at a striking velocity of .371 km/sec (1220 ft/sec).

Case 2. A Bearcat rod with a hemispherical nose impacting a 1.27 cm (1/2") aluminum target at a striking velocity of .343 km/sec (1125 ft/sec).

Case 3. A hollow Bearcat cylinder impacting a 1.905 cm (3/4" aluminum target at a striking velocity of 1.22 km/sec (4000 ft/sec).

Case 4. An ogival projectile with an aluminum core and a tungsten carbide sheath impacting a 2.54 cm (1") target of rolled homogeneous armor at a striking velocity of 1.372 km/sec (4500 ft/sec).

Case 5. A hemispherical cap projectile with a tungsten alloy core and a maraging-300 steel sheath impacting a .9525 cm (3/6") target of rolled homogeneous armor at a striking velocity of 1.524 km/sec (5000 ft/sec).

Target-projectile configurations are shown for each rase. Sketches are not to scale and all dimensions are in centimeters.

35

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47

^^^^^ inn i i i „ ^

4.3 Diagnostics

TOO MANY POINTS ON INTERFACE OF MATERIAL XX WITH MATERIAL XX - In subroutine ADJINT when attampting to replace the interface boundary points of material 2 with those of material 1, the material 2 boundary would exceed it's maximum allowable size,, Rerun allowing for more points on material two boundary,

AT POINT (XX,XX) IN FDIFF AT T-XX.XXXXX STAB-XX.XXXXX MAT-XX - Solution may be going unstable at this point. If it does not correct itself try larger artificial viscosity coefficient.

AT POINT (XX,XX) IMAGINARY SOUND SPEED IN FDIFF MAT=XX ESY=XX.XXXXX T=XX.XXXXX - Solution unstable at this point and will be recomputed in ONESTP. If it does not. correct itself try larger artificial viscosity coefficient.

AT POINT (XX,XX) IN ONESTP AT T-XX.XXXXX IPOINT=XX STAB-XX.XXXX RHO-XX.XXXX U=XX.XXXX V=XXoXXXX DELA-XX.XXXX DELB-XX.XXXX B SUB R-XX.XXXX MAT-XX - Solution may be going unstable at this point. If it does not correct itself try larger artificial viscosity coefficient.

AT POINT (XX,XX) IMAGINARY SOUND SPEED IN ONESTP RHO^XX.XXXXX U=XX.XXXXX V=XX.XXXXX T=XX.XXXXX MAT-XX - Solution unstable at this point and will be re- computed by interpolation. If it does not correct itself try larger artificial viscosity coefficient,

AT T-XX.XXXXX DENSITY DOES NOT CONVERGE ON MATERIAL X BOUNDARY AT POINT XX - In subroutine DENSB or subroutine INFACE iteration for density to obtain pressure that satisfies proper normal stress boundary condition does not converge. This is usually a sign of an instability in the solution.

MATERIAL X BOUNDARY EXCEEDS DOMAIN - RUN ABORTED (ZMAX,RMAX)/(Z (I) ,R(I)) - A shift was attempted in subroutine FINISH but there was no room. The boundary coordinates are printed in a-3 space. The minimum is zero and the maximum is the printed value. Rerun allowing more points in the proper coordinate direction.

AT X=XX MATERIAL X BOUNDARY CROSSED MORE THAN X TIMES T-XX.XXXXX - The boundary crossed a mesh line more than the maximum number of times allowed in subroutine BPOSN. The boundary points should be examined to see if this indi- cates an instability or if more crossings should be allowed.

48

qummmmmim ' n i "j'""l,",L1i"-1"1 "i»!« in i mmi iiiwi - imww.nip i. 11^

bäääA

4.4 Sample Output

A sample of the output for the two Silver Bullet runs (6.0) follows. The Input data for all materials appears first. Printer plot and printed output at each selected time interval will appear next. The printed output is described in the writeup for subroutine OUTPUT in Section 2. A listing

" the complete output for the two problems at time t-0 is given.

49

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PROGRAM LISTING

9i

"■ "NU II HWI" «»"« ' U' n in .1, i mi. i «^

PROGHAh SMlTEdNPUT,OUTPUT,TAPEl,T»Pfc2#TAPE9 ■ IT)

COMMON /COEVAL/ KT#AKT,PT,L'TmN,ITER,NEIB»,IPO iS.TOP.CAL.KHAX.PURG.HSCL.Lb.Lr

COMMON /MATARR/ NMAT, IM*T(1?,5),FMAT(23,5>,MAT COMHON /TVALS/ IST*RT,TMAX#TPBIM#TFRPL.TPL0T,T UOGICAL ERR CALL IMTAL TPRN « AKT*TPRIN TPRT ■ AKT»TPBPL TPLT ■ AKT*TPLüT TSVE ■ AKT*TSAVE

10 KT ■ KT*1 DT « l.OEö DO 20 MAT « l.cJMAT IF (FMAT(?2,MAT),Rfc,lT) ßi) TO 20 ÜT • FhAT(2?,MAT) MT ■ HAT

2ü CONTlNLiE IF (UT.GT.DTMIN) (!C TO 30 22 » FLOAT(IMAT(ö.fT>-l)«M''*T(l.MT) RR « FLOAT(!MAT(V,MT)-2)«^HAT(2iMT) -Rl'fc (6,120) AKT,fT,;ZiBW,PT GO TO 100

30 AKT « AKT»DT CALL MVSMC CALL ADJINT CALL B0NDRY CALL DENSE) DO 40 MAT i l.flHAT CALL GENVAL CALL FDIFF CALL FINISH CALL RPOSN CALL BVALU CALL INTHPL

40 tüwTINUE IF <ERH) RO TP IOC CALL SECOND (T) IF (T.GF.TCOMP.OH.AKT.GF.Tf.AX) GO TO 90 IF (AKT.LT.TPRT) OC Tn bQ CALL PRNPLT TPRT ■ TPBT*TPRPL

90 IF (AKT,LT,TPLT) GC Tn ftc CALL PLTOUT TPLT ■ TPLT*TPLOT

63 IF (AKT.LT.TPPN) GC TO 70 CALL OUTPUT TPRN z TPRN«TPRIN

70 IF (AKT.LT,TSVE) 'SC Tn «0 CALL SAVE TSVE • TSVc^TSAVt

flO SO TO 10 90 IF (TSVE,LT.1.0EB) CALL SAVE

100 IF (TPLT,GE,1.0FB) f.O TO HO CALL PLTOUT

INPUT,TAPEA » nUTPDSMlTb ? S" |TE 3

lNT,ERR.EPS,EPSl,RDlCni 1VAL 2 ClfVAL J ■iATAHP ?

3AVF,TCn''P,TZ TvALS ? 3M ITE 7 S»' ITfc B S" ITE 9 s« ITE 10 s« ITE 11 s- ITE 1? S" ITE n SH ITE 14 S" ITE 15 S" 1Tb 16 s-- ITfc 17 Sv, ITfc 1« S" He 1" S" ITt 20 S" ITfc 21 S'< ITfc 2? b" ITE 2,1 3'<; iTE 2« s-: ITE 25 s- ITE 26 sr I'£ 27 S-! ITfc 2fl S-] |Tc 2» S"| ITE 3n S«l ITE 31 S-i |TE 3? s-i ITS 33 Si] ITfc 34 s-i ITfc 35 S"l |TL 36 S"l iTE 37 SM iTE 35 S>1 ;Tt 30 SM] TE 40 S'l rfc 41 S"l TE 4? SKI it 41 S"l TE 44 Svl Tk 45 s-i Tfc 4* S-I T£ 47 S'-l Tfc 45 S»!

Tfc 49 S' I TE 50 Si I Tfc 5' s-i TE 57 S' I Tfc 53 S-I Tfc 54 S"! IE 55 s-i Tfc 56

93

Preceding page blink

110

120

»ND rue 7 IF (TPRT.LT.l.OFB) CALL HHNPLT |F (TPRN.LT.I.OEÖ) C*Ll OUTPUT STOP

S'll S H

SMI S"I

FORMAT (6H04T T«F«,:<,?7H STHP TOO SMALL IN M*T£H I *L 12.16H AT POINTSHJT 1 (Z.R)"2EU.4.5X3Hi;T»6ll14)

:, '' fcND

ITfc

57

60 61 6' M

S-ITE 64

94

■ ""■" »w»

SLdPOuTINE INITAL CCMMON// w(22D0i/)fL(?2P0) CCrtMQN/BNüCRS/ waI(10,».«,7),Pnl(lO9,£),I^n(l?<,,,'),

lrtbJ(78.8,7)#ppj(7fl,«).JND(7«,9) CCnMQN /BNDVAI./ ^R(A0Ü,7),rRX('.OO)»rPY(6P0).rRS(6C0)

IMTAL PvTvAL b^,Uf^ S BKUrHS BNUVAL

CCrtMuN /ZONFS/ NBPG<5i3).NrNr<5f3).APCSIZ(5i3J.Iil«MAX(5i3)#riSMlN(ZrnFb ; 15,J> ZCNFS .

CCMMON/MSMrCN/ Y(78>,ÜY(78>,EVA(7fl),FSY(78)|V«!F(7»<),F«YA(78), h«!HFCN ^ lYStA(7Ö)ieSVE(7B)>El3F(78»,Af:r(7e),*yY(7e),ASYA(7<») MSHFCN ?

CCMMCN /MAT4RP/ NM*T,IM*TJl2»MifM*T<23.r),MAT MATARE. ? CCn^ON/SCWTCH/ T^n(^C0,7),TFrx(3OO),'FRY(30O) SfHTO ? CCMM0N /"ÄTVAL/ AX,AY,CrL.Vir,VlST,Mt,VC,PHO,XO,po,TC.XZ,A,B,AHL.DMiTVAL '<■

lAPu.CHAM,rtMAX,FA:T,»Na,AF,SP",ALiAS,AK,HAL.HA'5.HAI',rAL,'3AS.OAK,DAXMATVAL •* 2iCAV#HUAX»HPAV,nA)(2,DAV^,HDAXV,0DAyV,iTR,HALF,,U.T-TrML,rPTrMUi0nVMMATVAL - 1U. il:'fcnTM,N[#Nj(NrHAX,|S,jS,IJt'.,IBS,If;R,jSP.NrH,MjMl,»D.Nnl.NF,^f^AT'A!, •- «,N^ ,MIP2»'JTR MATVAL h

CLMhO^J /PHESS/ PDFR,PW,PE,MA"''0 PCtSb :• CCiMüN /fcUSTP/ API .iO).RPL<i: >.APB(ir ).PPP(i;>.AU',H(in).PFT4(lO).Ffc^S>1fi '>■

isdPj.tzfcMOdOiEspt-MUo.pH^/podO.pM^dO) fcr.üTp ;< CCMhüN /THCPRT/ NTR^(5>, ITP(r.25)iTRF(5,25> TRCPPT . CCMMOKJ /COMVAl/ KT.iKT.nT.TT ' »N, I TfP, NE IF"» IpOP*T,ERS,ERS,EPSl» "DI C0«VAL

IS.inp.uAuiKMAX.PORG.PSCL.Lr L- CDMVAL CCMHQN /TViLS/ ISTART,TMAX,,." I N, TPRFL» TPLOT, TSAVF, TCTM», TZ TVALS \- CCHNQN /INTFC' MMFr. INfCJöüJ.NONIMCCO,") PTfC .' DMfNSlON TITLE(2n), AMAT(2l) JuITAU? ECufVALENCE <AMAT,AX1 IMTAL:*- ECüIVALF'MCE(V7,T0) orA)( - REAL Mo I^ITiLl1' LCblCAL PEER,ERR IMTALZf DAiA KT,AKT,0T,ERR/n,f,0,0,0,.FALSE,/ IV1TAL23 DA l A Pl,AX,AY,BDIS,-,AL,'3S.En«;i,KMAX/3,141592653,l.n,t,!J,r,?5,n>25IMTAL2?

i.o.Gonui,o.noGi,7/ IMTALZJ

ETAIY) = dM*x-ALOl".(«B*A-Y)/(r-A»Y))«A(JL IMTAL2< ALH(X,Y) « FArT«tX-AN(i«Y«TOP»ATAN(Ar«Y)) I'JTALZ-

CALL stcuND (TZ) !!iI*!-?C RE*Ü (5.420) TITLF IMTAL27 wRlTfe (6,«30) TITLE IMTALZf- hEAÜ (5.410) TMAX.TBRlN,TpRpL.TPLOTfTSAVF.TCr,'P,p1RC,P5CL IMTAL?« REA[](5,41Ü) PHIS IMTALJl KEAP (5.J90) '-MAT.ISTART IMTALJ1 READ (5,400) MNF- T IT/LJr Nl <fr « 5«NlNFf IMTALJ-S RfcAli (5.400) (INFCCD.I « l.MNe) IMTAL3« DTriN » 1 .OECi I" ITALJ"? IF (ISTAHT.EO 0) f.O TO 1C I'.1TAL3^ RF-INP I IMTAL37 READ (1) KT,*KT,DTMIN IMTAL3' READ (i) NlNFCNl'.ö.tlNFCd»» I • 1,MN6) IMTALJ"»

10 DC 030 MAT ■ 1,NH»T l\'ITAL41 REA[i(5,l»0) M.MJ.ir.IL.jF.JL.NLF.KTr.KBT.NFVAX.NTR.HATMC.IPMNT, OF A/

IJPHINT

READ (5.410) ZLES.YNAX.THETAiCAR.D.VIS.vnT.CfL REAl; (5,410) klu.^C,RHn,iJl IF (MATNJ.GT.C) GO TO 20 MAi»'0 ■ -MAT\n HEAD (5,410) APLCATNnj.BPLC'ATNOj.ArpCATMOl.BPP'MATKOl.ALPl- (H»T^

OFM MTAL43 ' ITAL*4

MTAL45 VlTAL4^ '.1TAL47

95

10).PfeTA(r1*TNC),ES(MtTNO).EZFnn<MATNO),ESFRH(MATNOI,riUNIhATNO) ^jJ^IJ

HHU2H0(HATN0) ■ «MO iNlTAUbP 20 WfilTEN(6,«40> MAT.Ni,NJ.lF,lL.JL.ZLEV,VMAX,THETAtCAP,tl,WlS.VtST,CFINlTAL51

IL.MU.VC.HHO.UI MlTALb? D(; '« » ' l'7 UTALS«

30 IHATU.MAT) . 0 PM TALb' DC «0 M ■ l.MAT „ TAL^ IP*T<4,MAT) ■ :MAT(«,MAT)*1MAT(1.M) ., T!IS;

IKAM5#MAT) . 1MAT('5."AT).IMAT(2,M) , _ L TilH" 1KAU6.MAT) . iMAT(A,HATW(I"ATa#H)*2)MMAT(?,M TAISV

40 IHAT|7,HAT) ■ IMAT(7,H*T).IMAT(3, M) v T*rÄn IHATd.HAT, . NI \;^tl

N*SNJ*1 IJITAL6^ IKAT(2#HAT)-NJ M TAL6< IMAMS.MAT) . sr«AX ,; ^ IKATdO.-AT) . MATNfl »- TALob IKAT(U.MT) • IPRIK.T . TAU* IMATdü.MAT) . JPRI^T M TALft7 NI^ • Nl*2 ' TAL6b IS • IMATU.MAT» « TAU69 JS • IMATCS.HAH L TAL7r Iwb • lMAT(6,rAT) -. TAin IHb . MAT(7.K*T) . TAin DC «.0 J » l.NJ .' TAL7^ J^=IJS*(J-1)«MP2 MfTAI7« DC M, , . i.M }.;lTAt7b Ii,-JJ*J I<iITAL7^ DC 50 KK « l.KMAX N1TAL77

50 WdJiKK» « O.r 11TAL7'' 60 L(lJ> • ü IMTAU79

DC 70 I . l.NFfAX "is TALBO FSXUBiM) • CO ' TALH1 FBy(l«S*l> • CO <1 TALB? FRidfl!.*!) • CO ■ITALB1

DC 70 KK « I.KKAX .■ TALfti 70 weilaS^I.KK) »0.1 . \,k\ uc

XO . ZLFN/FLO/TCIi-.m, \s\\\l*t TO » XU 1MTAL87 u0 ' Xü/T0 A He PD a RMO^UQ*«^ {«ITALH« FAoT . 1,0/XO MTAL90

"L * ^/P0 v, TAL91 YC » YC/PO MTAL«? rc - crc..2)/7. \

READ (&.410) (FRX(I),rRY(I).l»lTl,lT:) \t\\r\ A NHlTt(6.450) (FRX(l!.rRV(n.:.lTi,ITr> . TAU9& N1 • NLr IÜITAU96

ITI.IBS*NI ,ITC , IT^.Ifl!,*N2 . ' , , HMD (b.410) (FPxm.rRydj.l.lTi.lTD vinct

96

c IMTALV

(FRX<n,FRym,I»ITlilT2) (FRXm.FRYm.l-ITl.lTD (IT«(MIT.I)»I • l.NTR)

» l.NTR)

N2 ■ N2*NRT- 1U»1H!)*N1 IT^«JBS*N2 READ O.410) HR|Tb(6>470) READ (J»,J90) DC 60 1 ■ l.NTR TRblMAT,I> ■ 0,0 J = ITH(M*T,I) TFrtXU) » rRX<lBS*J> TFrtYdJ ■ FRY(IBS*J» IF <J,NF,N2) GO TO «0 ITw(MAT,|> ■ J-l T«b(MAT,|) ■ 1,0

80 COTINUF wfilTfc (6#48n) ( l.TFPXdJ.TFRYd).! IF (IST*HT.t-:Q,0) GO TO 100 RfcAD (i) {NBEG<M*T,I)iNFNn(HAT.I).ARrSlZ(MAT,I).

INF.YZ ITi»JBS,*l . ■<i«IRb*NF HrAD(l) <(WB(I,KK),KKil,KMAX).FRS( I),I■ITl»1T?),

1I«1T1,JT2).DTM REAC (1) NTR, (ITR(M»T,n,TRS("AT.I), I ■ l.NTD 1^ ■ IF-l I? • MIMUF JCH «JF-1 j2sMj*jOF DC 8b J=JF,J2 JJ=IJS^(j-l)»rvIP2 ITi«jj»ir n<i»JJ*IÜ

85 READCI) nw<I,Kt«),KK«SKMAX),l.(n.l«ITl,lT2> NC » NfcNÜ«M*Til> NE • NfcND(MAT.2) ZD^ ■ FLQATCIDFI»AX

XZ » Xi>ZDF RCi-«FLOAT(JDF)«AY Y2sYZ*KDF DC 90 I s l.NF Ffir<inS»*J>«FRY( !9S*t)*RDF

90 FRX(IBb*I) ■ Fpx(IBS*n*ZDF 100 CCNTINUE

JUtJ « THETA»PI/IPO.

BHAX»FLnAT(JL-jF*l) Y0 ■ YMAX/(BHAX-0,5» AKb ■ l./TAN(THET) CFL«CFL*X0 AF » 1,0/CAP TCP ■ 2./PI A = Y0«BMAX B » A/(l,-D/A) APL ■ ÖMAX/ALOG(«B*A)/<P-A>) DAUU ' 1,/(2.*B*ARL) CNAN > ( (U*A)/(B»AM**(1.0/BIIAX) IF(ISTART,NF.0) SO TO 115

(FRxm'.FPYd),

IMTAion

IM1TC1 - IMTCll'1

If'ITCHt IN'lTCll? INITA105 IMTAinl

INITAIO'J IMJTAIO* IMTA107

INITAIO*" IMTA1U'3

1N1TA11 ) TJlTAlli 1NITA11? IN1TA115 IM I T A11 1

I « 1.3».X7.MI,HJ. I'llTAUS OTAX » 1N1TL11.5

IMITCU< 1MITC115

IMTCllft rJlTAll«? IN1TA120

IMTA121 OFAX 3 OFAX 6 OFAX 7 iMiTcua INITC119 INITCIZP IMlTC12i P'lTAl?-! IN1TA12!5 lNlTA12ft IN1TA12V OFAX f OFAX ') l\'lTA32fi OFAX 10 IN1TA12<' I^'ITAiau IIMTA133 OTAX 11 IMTA1J3 IfJlTA134 OFAX U IMITA136 lnITA137 lNlTAl3fc IMTA139 IMITA14I IN1TA145 INITA142 IMITA143

97

i ■*t.

FBY(IBS*I-1))**2*

ZK1N ■ 1,0610 H^lNiZHlN DO 109 lal.NZ ZZ « FRXJIBS*!) RH ■ FHV(IBS*I) ZKiN ■ *MIN1(ZM1N,Z7) RKlNtAWlNKRHlN.«») FRX(|BS»1> ■ *LP<ZZ.Rn)

105 rHY(lBb*lJ ■ ET*«RR) XZ ■ <FL0AT(IF)-l,5)**X-fACT«ZMlN FRX(IBb*l) ■ FRX(IB«*1)>X> YZ'«FL0*TUF)-1,5)«*V-E7*'RMM) IFUF.bO.l) YZsO.O FRV(IBS*1)»FRV(!BS*1)*VZ DC 110 HÜ.N2 FRX(IPS*l) ■ FRX(IÖS*I>*XZ Ffi''(IBS*n»FRY<IBS*n*VZ

110 FRs<lBS»n ■ FaS(IB«!*I-l>*?orT((FRY(IHS*I)' 1(FKX(1BS«I)-FRX<IPS*I-In««?)

NC ■ 2,0*FRS<I8S*NLF)*1,5 HI • NLF«NTP-1 NE ■ 2.0«FRS(IBS*M>*1.' NF « 2,0«FRS(laS»N2)*l,5 NetQ(MAT,l) » I NBt:Q(MAT,2) > \D NStG(M*T,3) ■ \F NEND(HATil) • \D NENDJM*T,2) ■ NE NEND<MAT,3) ■ NF

115 CONTINUE DO 120 I ■ 1,21

120 F^AT(1,MAT) * AMAT(!) FPAT(22.MiT) « 1,0 NTHS(MAT) ■ MR CALL GfeNVAL DC 130 J ■ 2,Nj AJ*AY*KLOAT(J-2)»vZ CW ■ CHAN«*(BMAX»AJ) Y(JS*J) ■ A-B*(CH-1.)/<CH»1.) YSt(JS*J) ■ FACT*(B««2»<A-Y(JS*J>)**?)*DAnL ESYljS«J) ■ 1,/YSE(JS*J> AFT ■ AF«Y<JS*J) AFY2 ■ A>Y««2 ASY(JSO> ■ ANG*TOP»(ATAN(AFV)*AFY/(l ♦ArV2n ..ry^wM AYY(JS«J> ■ xO«2.*ANQ«TOP«AF«YSE(JS*J)«<l.-AFY2/Clt*ArY.»))/(l,

1ESYE(JS*J) ■ -2,«DAnU»(A-Y(jS»J))*ESY(JS*J) EIüF(JS*J) ■ SORT(ASY<JS*J)««?*l.) IF (J.liT^) DV(JS«J) ■ XO«Ysn(JS*J>/V(JS*J) IF (J,b0,2) DV(JS*J) ■ 1.

130 CONTINUE Y(JS«U ■ -Y(JS*3) YSt<JS*l) ■ YSE<JS*3) ESY<JS*1) ■ 1,/VSE(JS»1» ASY(JS*1) ■ -ASY(JS*3) DTUS'D ■ -DY(JS*3>

♦ AFY

INITA144 OFAX 13

NITA14^ N1TA146 INITA147 IMlTA14h

OFAX 14 |MITA14<* INITAISP INITA1Ö1 INITA152 OFAX 15 OFAX 1<> OFAX 17 N1TA15.* NITAIS«

OFAX IP 'JlTAlbO NITA156 NITA157 N1TA158 NlTAlb'i' NlTAlöf M1TA161 MTA162 NITA16J NITA164 flTA165 MTA166 MTA167 N1TA168 fJlTA169 MlTA17n

NITA171 NITA1/2 faTA173

OFAX 19 NITA175 N1TA176 NITA177 NITA178 MTA179 MITAIBO NITA1H1 NITA1H2 NITA183 NlTAie* NITA185 NITA186 NITA1B7 NITAIBB NlTAie9

NITA190 N1TA191 NITA192 NITA193

98

'^■-r'--- flii/lürt

DO 1«0 J ■ 2,NJM1 iri3Aian Aj»*YMrL0*T(J)-l,5)-y2 TMITAIO^

yy ■ *-B»(CH-I.)/(CM*I,) JiiltJoI yst*iJb*j> ■ ,5«(ysF(Js*J)*ySF(js*J*i)) I.Jor feSY*uS*J> ■ l./ySE»(JS»J) K M Ilinn ASt»us»j) • *NO*TOP*(AT*ij(*r«YY)«Ar«yy/<i,*(Ar«yy)*»!?)» ! , tl«? DY*«JS«J> • X0«VSEA(JS«J)/yY INJTAZ01

140 CONTINUE }M}Tl?n3 YStrAUS*l> ■ ySEA(JS»2; INJTAZDJ feSY*(jb*i) . ESYA(JS*2) i'J!!l?n* AST*(JS*X» « -ASyA<JS*2) I on! DyA(jS*l) ■ -DYA(JS*2) !!»,„, IF (ISTAHT.NE.Q) RO TO 260 !.!2u DC 240 M • i.30 J TA2

GC Tu (WO,180,190). M {.,!.,,,

BC TO ^0U IMTA21Z ien LF « LU*NTP.1 I^ITIPM

Ü0 TU 200 M TAPit 190 LF » La*NRT-l M TA916 200 LAUD . NfcND(MAT.»1)-LF M I*,:,

If ■ Ht-ir IM1TA217 IF (LM.EU.O) Gü TO 240 IIÜT^I« DC 210 I • l.NTR M rl^O IF UTH(M*T,n.LT.LF) GO TO 210 l« !!!,« ITK(MAT.1> ■ lTR<MAT,I)*LADO L, I*,,,

210 CONTINUE WirlUl NIN2 » 2»NINFC }. ,i,oI DC 2Un I ■ 1,NIN2 XJTAI« IF <IN>C(J«I-2),ME.MAT) SO TO 220 l% HI IF (INFCOM-D.GE.LF) INFC(3.I-1J ■ INFC (3« 1-l)*LArn Mi?!«? IF (INFC(3«1).GE.LF) INFC<3*I) ■ INFC(3*I)*LADD IMITA227

220 CONTINUE iNlli?!"

DC 230 LL - l.LM TI^I

^ ' NK1-LL T1?32 L2 » L1*UADD \t\Al\l

Ffiy(IRS*l.2) ■ FPY(IBS*L1) ^ !.,« 230 CCNTlNUE Wtlälll

240 CALL RfeLAÖU (M) ^ TA,tp DC 2b0 I • l.NF WlAllo weilHS^I.l) . 1.0 M TA3«n WBUHS*I,4) . 0.0 WIVAAI

250 WB»IÖS»I,Z> « UI M TA54? 260 CALL BPOSN M TAS43

CALL BVALU WlAlA IF (ISTART.NE.0) GO TO 320 M.TAO!^ DC 2Ö0 J - 2.NJ \l\ltlll JJ=IJS*<J.1)»NIP2 \n\Al47 DO 280 1 - l.NI J rlllh

W(1J,1) ■ 1.0

99

IMITA249

M<iJ,2) ■ UI DC 27(1 KK ■ SiKMAx

270 M(IJfKK) '0,0 KlJ) ■ 1

280 COTINUB C*LL IHOSN DC 2V0 I ■ 1,N1 WUJSM.ll ■ W(IJS*?«NIP2*I,1) WtlJ8*l»2> • W(IJso«NlP2«I,j:) «(US^l.J) ■ -W(IJS*2»M1P?»I,?)

290 LIUSM) • L(ljS*2«MIPZ*l) SB'1 a u.U PttH • .TRUF. DC 300 J ■ 2,NJ jj=IjS*(J-l)»NlF2 DC 300 I • l.Nl IJ=JJ*1 IF(L(IJ),tQ,0) 00 Tf) 300

6 ' W(IJ,4) P = PR!i(HH0,E) C? » PW*P*PE/RH0**2 C = !>QHT(C2) UC « (AB!»(W<IJ,2)-*<5Y(JS*J)*,.'(lJ,3))»Eir1r«jS*J)*r)«r,AX VC « (ABS«W(IJ,3>)*r)«ESV(JS* ))«D*V SR » AMAXKUCiVf) IP (SB.LbiSBM) GO TO 300 S6^ ■ SB ISd « I JSU a j CCNTJNUE UC 3X0 M ■ 1,3 NKd ■ NBfcG(MAT,M) NNf ■ NEN0(HAT,M) *RCS1Z(MAT#M) ■ FRS( IBS*MNF)-rRS(IPS»NNP) DTM ■ CFVSBM DTMN « AMlNKDTM.nTMN) fMATt22,rt*T) « DTM

300

310

320

330

340

350

360 370

380

1HAT(8,MAT> ■ IS3 |MAT(9,MAT) ■ JS§

CONTINUE If (ISTAHT.EQ.O) DTMIN « 0.0F*DTMN IF (TSAVb.LT.O.O) TSAVt ■ 1.CF8 IF <TPHPUiGE.0.O) GO Tu 340 TPHPL • i,0F8 GC TO 350 CALL PHNTS (999IT1TLE) CALL PHNPLT IF (TPLOr.GF.0,0) GO TO 360 TPLOT » 1,0E8 QC TO J70 CALL PLT0UT IF (TPHIN.GF.0.0) GO TO 380 TPHIN • liOEB REIÜKN CALL OUTPUT

INII rA2Pn INII rA?Pi INII 'A2i)2 INII 'A29S I Nil rA2!>4 IM1 'A?!)^ IM1 rA2S6 I Ml A?S7 I «'11 rA?bP INII rA2b9 INII rA26C INII rA2M IMII TAPft? INII A?bi nn rA?64 IMl rA?fcb i-n 'A?66 IM1 C12? P'll 'A267 INII rA26P INII •A269 INII rA270 »Nil rA271 INII 'A272 I"' 11 rA?73 INII rA?74 INP rA275 INII rA2;t INI rA277 I »J 11 rA278 IMP rA?79 INII rA2eo IVI1 rA2öl INII rA?e2 I Nil rA2Hi JMII rA2B4 INI' rA2e5 IM! rA?ö6 INH INII

rA2B7 rA2B8

INII INII

rA2B9 rA290

INII rA29l INII rA2<'2 INII rA2«J3 IMH rA294 INII rA295 INII rA29(S INP rA297 IMl rA?9e INI' rA299 INII rA300 INI" rA301 INII rA302 INII rA303 INII rA304

ICG

390 FCKMAT 400 FOHMAT 410 FOHMAT 420 FCHMAT 430 FCKMAT 440 FCHMAT

REIUHN INITA3n5 If;ITA3nt

(X6I5) IfUTA3n7 (1219) lNlTA3rP (»fcl0.3) INITA3PV (20A4) IMTA310 (iHl/lH020A4» INITA311 (1«0//58XBMMATERIAU?/5X19HHAXIHUP ALPHA MESH» I 4', 17)(l8>iM*X I INI TA312

IMLh BETA MESH»14,18«2«HIN1TIAI. LEFTHCST ALPHA L lriF»I4/5X29HIM TI AL IM TA313 2 RIGHTMOST ALPHA LINE«I4,7X?6HINITIAL TOPMOST BETA L^E«l4,10X27HIINITA31< 3N1IIAL MATERIAL TMirKNFSS»F7,3/5X24HINlTl AL PATEMAL MEIGMTIFB . 3,»! I M TA31& 4X13HMATERIAL ANOLE"r7,2ilflXllHCAP LEK0TMiF9,r/5>(2^HR0l. NnARY L*YER lMlTA31fc 5THCKNbSS"F8.3,7X30MONE«?TEP VISCOSITY COCrF IClE'JT-r* . 4,4X30HTUOSTE IM TA317 6P VISCOSITY C0EFFICIENT«F6,4/5X17HTIPE STFR FACTPR-FS .SilflXH^SHEA IMTA31b 7R M0BULUS"F9.5,17X16HYIFLD cnilDITI0N.F9 .5/5X25HIHIT I AL MATFRIH DEP'lTASl" 8NS1TY«F7.3,8X26HINITIAL MATEPIAL VELCCITY"F9,6) INlTA3J'C

450 FCKMAT (1H041X47HINtTI AL (Z.T) COORDINATES OF LEFT MATERIAL FACE/(IMTA3Z1 15«/X,2M,Ö)n IMTA32^

460 FCKMAT (1H041X46HINITIAL JZ.D COORDINATES OF TOP MATERIAL FACE/(51NITA32J l(7X,2Fy.5))) INITA321

470 FCKMAT (lH040X«flHirjlTlAL (1,?) COORDINATES OF RIC"T MATERIAL FACE/1MTA32^ 1(517X,2F9,5))> IMTA326

480 FCKMAT (1H043X45HINITIAL (Z,") COORDINATFR OF TRACER PARTICLES/(5 ( IMTA327 14X.I2IIH>,2F9.5))) IMTASZH

fcNU IMTASZ''

101

**■ ■*■■*.- äuim

3

SUBROUTINE GENVAL . VS\ut> \ COMMON /MATARR/ NMAT.lMATda.SJ.r^mjjJJ.MAT ioMAtfjl| ,% ...„.„^ÄNES ? COMMON /ZONES/ NU6Gl9.3)»NLNB(9.S)#^CSlZ(5.3>.nlSM4X(9,3),ni«MtN(Z2NES ?

19 3) ZONES 3

»« äK; M'TAW!»!;:.«.«^-«.« «•.-»-«•:":[i iS.TOP.DAL.KMAK.PORC.PSCU.LBtUr cnwv.L

C 1 2 3

COMMON /PRESS/ PUEP.PB.Pk.MATNO ^=" ? COMMON /INTfC/ NINFC•INrC(60>,NONI^<^0,9) irvWAHn OIMENSION AMAT(21), MMAT(7) QCVVAI 11 IQUIVAUENCE (AKAT.AX). (KMAT.NI) GRvlu? PP**- MV . QF\VAll3 ÜO 1U I ■ 1.21

DO ?U | ■ 1,7

N!M1 ■ Nl-1

ÜFNVALK 10 AMAT(I) ■ FMAKI.MAT) GFNVAL15

QtNVAl.16 2o MMAT(I) . iMATd.MAT) ^:::r::

MAJNÜ • iMATdO.MAT) GFNVAU17 DAX « 1.0/AX GPNVALl« DAY • 1 O/AY ÜFKVAL19

MDAV • O'.S.DAY «NV 1.21 0AX2 - DAX«»? V£lk\\\ DAY2 « DAY-.2 UFNVA123 HDAXY • 0.5.DAX*Ü*> r\ll\\\\ ÜDAXY ■ 3.5.H0AXY fcV^W HAUfHU ■ 0,9*MU (.ENVAL26 TWTDMU . 2,8-MU/3.C r^ül-!!

TREOTM « 3,0/<2,0«ru) S^!*L5? AK.FACT'DT 2 * , AL • AK*DAX QENVAL33 AS - AK.DAY V?lkyA MAC ■ fl.SaA« GPNVAl.36 ÜIS - 0 ?:" ^NVAL37 OAL • 0,25«AL arNVALS«» SAS • 0 25*AS 8ENVAL39 WAK « C.25.AK QFNVAL40

(JENVAL43 NJM1 ■ NJ.l 0ENVAL4« ND • NENÜ<MAT,1> QPNVAL45 NE ■ NEND(HAT.2> QPNVAL46 NF « NEND(MAT,3> (JFNVAU47 NDl ■ ND*1 QFNVAL48 NEl ■ NEM 8ENVAL49 N?R - NTRS(MAT) G6NVAL50 PETUHN ÖFNVALSl iND

102

zäjtm.

IDBRUUTINE MVBNO , *M^ l COMMÜN /BNDVAL/ MB(»0n , 7) .r»-X(600) .rRV(600 ) .rR3(6nO > ^iOV*L ? COMMON /MAT*RR/ NMAT,lM*T<l2,9),rMAT<23,9).M*T „n.^ll^ l COMMON /COMVAL/ KT, AKT.DT.DTMIN,IT|R#N|IM. lPONT,ERR.e<'S,E''8l ,«»Dl^MV»L ?

lS.TOP,CAL.KMAX,PüRli,PSCL.La.|.F C''MV*1- 5

COHf '"" " ' " 1ARL. 2i 3Ui 4,Nr,NIP2.NTR ärii"''?? hOuIVALFNCE<Y2,Tü) 7* 0 " DO 10 MAT • l.NMAT v" ^

Nl ■ IBS«1 Hv^u in N2 • IÖS*NF M^^ 11 DO 10 I ■ N1,N2 •" u "

2P « XU.trRxm-XZNAMü.RU.TCP.ATAMAr.RB) ^BND 14

FR^I) . *.1AX1(RB*CT.WB<I.3).0,0> ZTull) 10 CONTINUE H;|^ J8

«PTURN M7BND 10

kND

103

mm* m ■ ^ „i

SLaROnTINe ADJINT »PJINT 2 COMMON /hNDV*L/ <IR(*00,7),raX<600),rPV<600),rRS(600) BNUVAL 2 CCMMON /M4TARR/ NM*T, IM»T(12,5),FMAT(23.5>»MAT MATiHR 2 CCMMON /iONES/ NBeG(9.!>.NENn(5.3».APCS12(5.!).DISMAX(5'.3).OISMlN(Z0NES ^ 15,J) ZO^FS 3 CCMMON/SCHTCH/ Ti<fl(10O,7),Trrx(3OO),TFRY(300) SCHTCH i COMMON /INTrc/ NlMrr.lSFC(60).NONlN(20,5) lNTrc ?

COMMON /COMVAL/ KT.AKT^T.DTMIN.ITER^EIPnjPHNT'.ESR.El'S.EPSl.RDICOMVAL 2 IS.IOP.Ü*L.KMAX,POPG.PSCL.LB,LF COMvAU 3 LCulQAL k»R APJIhT « DC 80 I • l.NlKfC APJINri" HAU ■ INFC(6*l-5) AOJINUl MAI2 • INFC(6M-2) iS^l^h

IF(M*Ta.feO,3) GO TO 3n AOJIIMTI?

Nl ■ IbSl*l AOJ'iKTl^ N2 ■ IbSl*NEND(H»Tl,3) AFIJIMI? Ml»lBS2*MrNf)(MAT2,21 *"

J'I!

:IJQ

M2»IbS2*NENt)(MAT2,3) *D'J' 'I*! ZKX2.0.0 APJ!KT20 DC 2 J.Mi,M2 AnJP:I"

2 Z''X2iAM*XX<rRX(J),ZMX2) An-INT2Z K«^! AnJlM2J DC A J.N1.N2 AnjlfTZ^ IFlFKXtJ) ,GT,ZKX2) r,0 TO 4 AflJlM?!) K,J AnJlNT26

4 CONTINUE AnJINT27

N2 = MtN0(K*l,N2) AEJ!M^ HMXI.0,0 AnjIf.T29 DO 5 J.N1,N2 APJir.T3

5 RfXl»AMAXl(rRY(J),RMXl) ^Ü^ÜI.l DC 6 KiMl,M2 APJINTi? IFirRY(K),UE.RKXl) r,0 TP ft Anjuns

6 CCNTINUF APJIUT3« 7 K.R*1 AnJINT35

a RHX2»AMAXl(FRY(K.i)lFRY(K)) AHJ!I!'l,!? Rh1>*2»AMINl(FRY(K»l>.FRY(K)) ADJIM37 Zh'X2«AMAXl(FRX(Krl),rPX(K)) {JHIUT« ZHN2iAMINl(FRX(K.l)1FRX(K)) AnJIMJV DC 10 J«N1,N2 ADJINT40 IFtFPY(j),GETRMN2.AND.FRX(J).r,E.ZMNJ) GP TO 11 AnJlM41

10 CONTINUE APJINT42 6C TO 7 AnJlNT43

11 J1«MAX0(J.IBS1*2> AOJIf.T44

DC 12 J«Jl,N2 ^,m5 lF(FHY(J),LT.RMN2,0R,FRX(J).f!T.ZMX2J 110 TO 12 AnJI.. ! j2sj ADJINT4n

12 CONTINUE IVtllltl J2=:MIN0<J2*1,N2) t2J, KTR, D.^RY(R)-FRY(K.1) ADJ^TSl IFUBStOJ,LE.l.OE-10J D-1.0F-10 AEJ,I.NI^ EHi:»(FHXlK).FRx(K.l))/D TK , ^.i IF(ABSIFM2),LE.1.0) GO TO 14 »S,,^TK* EH<:«l,0/tM2 AHJINTSS

104

■ ■«i. •-''., ..■". -jwt*

B2«rHY(K-l)-EM2«rRX(K-l) *D'!IM^ icu,2 AOJINTS? QO TO 15 AtUINTi«

14 B2»rRX«K.i)-EM2«rBY(K-ll tüÜiün

15 J-JzJl AnJINT61 DC 2t JJiJl,J2 AnJINT62 j.j.i gJ ,'1,J' AnJINT63 D»>RX(J)-FRX<J-1) »nilUlI^ IF(ABS(D),LE,1.0E-in> D«1.0F-10 .«..Sri! EM«(FHVJJ)-rRY<J-l))/D T«.^!? IFIABS(EM1).LE,1,0> QO TO IS A^^T^ 6K1.1.8/EMI tJJnTftQ IE»!tO*2 ADJlNT7o OC TO ^0 «JIJ.T/t

18 Bl«FRY|J-l).EMl.rRX(J-l) ", T,. lExJEQ AnJir.T7J

20 GO TO <21.22,23,24),IE tnnrT7S 21 R«CBl*tMX«B2>/(i,0-FMl»eM2) . .,!

GC TO 25 A0JINT7f 22 R»(EM2«91-EM:«B2>/<«sM2-GHi) ADJIN!!!

QO TC 25 ADJINT7fl 23 H»(Bl-B?)/(EM2-EHi) JUUIHr««

00 TO it AnJINTBO

24 R«(Eh2.Bl*B2)/(l,0-EMi«EM2) tlü!^», 25 lFlR1r.k.RMN2.AND,R.LE,RMX2) GO TO 40 .?,.;,?, 28 CONTINUE iljZlll

GO TO 7 ™J™ltt 30 Nl-IbSl*lNFC(6*lM) AnJINTB?

N2«IBSI*|NFC(6«I.3) "^/JIST M1«IBS2MNFC<6.I) inj NTB8

| M2«lBS2*|NFC(6«I.l) »«U^TBO M3=INFC(6M-1^1 knslJral M4.NEND(MAT2,3) tlV^rli LAUD»N2-N1-M2*M1 .„, TTOS NF = M4^L*DD tlVurll IF(NF,GT.IMAT(3#«AT?), 00 TO 55 {E, LTO^

DO 32 J=M3,M4 tlVtJrlt

TFKX<J>.FBX(K) ISj NT97 32 TFrtY(j).FRY(K) ^"ü^ioa

H5*M2^i.*DD JBN2*1 DO 34 KsMliMS

FRX(i).FRX<J) tSilHJ^ 34 r«r.K).rRY(J, JDjjNIOJ

nr 1* t>yJ u4 ADJIM05 00^36 J.M3.M4 AOJINIOÖ

FRX<K)«TFRX(J) tSJ,ll!J2« 36 FRT(K)»TFRY(J) iSji^Tng

H2»M2.1BS2 iSj wiSo lKhC(6«I.l)»M2»L*DD I* , *!:,, NEND(MAT2,3)«NF ADJlNlii

105

AHJlNTPe AnJINT99 AOJIN100 ADJIN101

ADJINUZ lMNkND<H*T2,2),LT.M2) 00 TO 80 AnJIMl3 NEND(MAT2i2»»NEND(M*T2,2)«LirO ADJ1M1* NBbO(MAT2,3)»NBEO<M*T2,3>«LArD ADJlNUi) IF(NtND(HAT2.1)iLT,M2) 00 ,0 «0 ADJIMl* NENDtMAT2,l)-NEN0(M»T2,l).LArD AOJINU? NBtO(MAT2,2)»NBE0(M*T2,2)*LArn AnJINU"

GC TO »0 AnJIMl« 40 NINT ■ J-l AHJIMZ') 90 CONTINUE AOJIMZI

|MC|Ml-i> ■ MNT-1B84 AnJIMÜ^ IN>C(6«I) ■ K-1BS2 A0J"a^: NF • INFC«6*I)*INrC(6*I-J>-l AnJIMZ" If (NF,LE.IMAT<3.MAT2)) GO TO 60 AOJIMZb

5> CONTJNUE APIJIMZ* WRITE 16,90J M»T?.HAT1 AOJIfUZ' ER* ■ .TRUE, ADJIMZ" QC TO «0 AHJIMZ«

60 NEND(MAT2i3) ■ NF AnJINU- IK^C(6«I-1) ■ Nf A0JIM31 K » K*INFC(6«N3) AHJIMJZ DC 70 J ■ Nl.NINT ABJIM33

FRX(K) » fRX(J) APJIMJS 70 FRMK) « FRr(J) AI5JtM36 80 CCIMTINUE APJIM37

HEIURN AflJJMäö

,0 F0HMAT (41H0TOC H.NV POINTS 0. ,NTEPr*CE OF KATEPIAU2.14M W.TH HAAOUINIJJ

iTEK!ALl2) APJlM^l EM)

106

.: ■■■u.—;...... irtniitt

SlöRüUTINE TDlfF rDIFF ? CCMMUN// w(22O0,7j,L(22OO» IMTVAL ^ CCMMON/MSMFCN/ r(7e),DV(7a>.rVAt7S),ESY<78>,ySE(78),ESV*(7e), HSMFCN ?

lYSt*(7«),E3VEI78),El0r(7JI),ASV(7B),Ayy<7l'>,ASVA(7«) MSHFCN i COMMON /M4TARR/ NMAT,IM*T(12,S),FHAT(23,5).HAT M4T*HR ? COMMON /COMV*L/ KT.AKT.DT.DTMIN.lTER.NEIBR.IPOINT'.EBR.EPS.EPSl.nDICOHVAL ?

ISi lOP.UAUiKMAX.PORQ.PSCL.LB.I.r COMVAL >) COMMON /MATVAL/ AK, »Y.CFL.VIS.VIST.Mt,VC.RHO,XQ.PO,TO, XZ,»,ö,ABL.OHiTVAL 2

lABL,CHAN,BMAX,FACT.ANQ,AF,SBH,ALiAS,AK1HAL,HAS,HAl'1CAt.OASlOAK,DAXMATVAL 3 2.CAV,HDAX,HDAV.0Ax2.DAy2.HDAXY,0ßAXV#DTR,HALrHU.TWtCMU,rRT6MU.60VMMATVAL * 3U. ISEOTM.NI.Nj.NFMAX.IS.JS.IJS.IBS.rSB.JSn.NIMi.MJMl.N'D'.Nrj.NF.NElMATVAL i 4.^^.N1P2|NTR MATVAL 6

COMMON /PHESS/ POER'.PR.PE.MATNO PRtSS 2 REAL MU FTIFf 1 LOülCAL PDER.AXIS FTIFF 1.) ÜIMENSION WW(3,3.7). F(3,3.7). 0<3,3,7>l M^.S^)', T(3.3.3) F01FF H DIMENSION WP(2,2,7)', UN<7) FniFF 1? SBM ■ O.ü FPIFF U NIH1 ■ Nl*l FnlF> 14 DO 10 I ■ l,Nl F01FF lb M = MPl-I F^IFF 1A DO 10 N ■ l.NJ FniFf 17 MN ■ IJS»(N-1)«NIP2*M F3IFF 1b L(MN*2) ■ L(MN) FniFF 1<3 DO 10 K ■ l.KHAX FniFF 20 W(MN*2|K) ■ H(HN.K) FniFF 21

10 CONTINUE FPIFF 22 DO 260 M ■ A.NIPl FDIFF 2J DO 260 N • 2#NJM1 FniFF 2* MK » |JS»<N-1)«NIP2*M FniFF 25 IF (L<MN),EQ.O) GO TO 260 FDIFF 26 NEIHR • 0 FHIFF 27 IF <L(MN*1)1EO,0) NPIBR ■ NEIFIR»! FP1FF 2H IF l\.tm»NlP2),EQ,a\ NEIBR • NEIBR*2 FPIFF 2V IF (UMN-D.EO.O) NEI«R ■ NEIRR»4 FDIFF jn IF <U<MN-NI^2>.EO,0> NEIHR ■ NEIBR^B FDIFF 31 IF (L<MN*NIP2*1),EOIO) NEIBR ■ NEIB«*i6 FDIFF 32 IF (l(HN*NIP2.1)lFO10) NEIBR ■ NEIBR*32 F01FF 35 IF (L(MN-NIP2-1),E0.0) NEIBR ■ NEI8R*64 FI21FF 34 IF IU(MN-NIP2*1»,E(M) NFIBR ■ NEIBB*12« FDIFF 35 IF (NEIBR,NE.O) SO TO 210 FniFF 36 MMü ■ M-2 FOJFF 37 NM<: ■ N-.J FDIFF 3P AXIS ■ .FALSE, FDIFF 39 IF (N,feO,2) AXIS ■ .TRUE. FDIFF 40 ESYN ■ FSY(JS*N) FDIFF 41 Djl ■ ÜV(JS»N)«OAK FDIFF 42 DJ<i ■ ,5«ÜJ1 FDIFF 43 PCbR ■ .FALSE, FDIFF 44 DO 20 J ■ 1,3 FDIFF 45 MJ ■ NM2*J FDIFF 46 YSbJ ■ YSE(JS*F«J> FDIFF 47 AR ■ -ASY<JS*Hj) FDIFF 48 JJsIJS*(MJ-l>«NlP? FDIFF 49 DO 20 I • 1,3 FDIFF 50 MI ■ MM?*I FDIFF 51

107

■a. liitüi

FDIFF &"! IJ»JJ»MI FOIFF S3 RMU • HdJ.l) FDIFF 5* U » h(lJi2) FOIFF 6? V » H(IJ|3) F0irF so E « N(IJ.«) FDIFF 07 SH • W(JJ.5) FOIFF So Si* ■ W(IJ,6) FDIFF y S2* ■ W(!J.7) FDIFF 60 P = PRSCHI-CE) FPIFF 6: WV.lI,Jil) • flHO*YSEJ FPIFF 6? Hhll.J.Z) ■ WW(I,J,1)»U FDIFF 63 WW(t,J,S) ■ HH(I.J.1)*V .„.i^iMi FDIFF 6«

Mhd.J,?) ■ S1WSEJ FDIFF 64 Hta( ,J,f> m S12*YSEJ FDlFF 6? m-i ,J,7 ■ S22*VSEJ FD1Ff 6H

fc s WWUiJ.O/YSEJ FDIFF 69 Fd.J.X) ■ WW(I,J,2»*AR*WW(I..I.3) Fp,Ff 71,

FdiJiö) " THTDMU*<?.»Ü-AR«V)«YSEJ FnIFF 74 FdiJib) • MU«<U»AR*V)*YSFJ Fn,Fr 7^ F(l.Ji7) « TWTCMJ»(9.**B«V-l)>*YSEJ F01FF 76 Hd.JiD ■ RHO«V FDIFF 77 Hd.J,*) ■ H(I,J#1)*U-S12 FDIFF 7b Hd.J.d) ■ H(I,J,i).V-2,«S22-Rll FOIFF 79 H(i.Ji4) ■ (E*P-S?2>*V-U«S12 FrjFF eo H<liJii) " TWTDMJ'V FDIFf Bl H(1,J,6) • 0. FDIFF «2 H<l,Ji7) ■ H(I,Ji5) FDIFF «3 Gd.JiX) ■ H(I,Jil) FDIFF B* Ci( I» J.2) ■ H( IIJI2) FDIFF Ho GdiJ.a) " H(l,Ji3)*P*SU*S2r FDIFF 86 0(1,J,4) ■ H(!,J.4) FDIFF Ö7 Gd.Jit») • -TWTDMU'V FDIFF OP ödiJ,6) ■ MU*U FOIFF 89 Qd,J,7) " FRTDMJ'V FDirF 90 Td.J.i) " S12 FDIFF 91 TdiJ.2' ■ -.5*<S11-S22) FDjFF 92

Td.J,3) ■ -512 FDIFF 93 20 "fx . ^BscF.J^a./w^s.s.n.n^i.n/wwj^!,;,, FO}FF 94

'ItiV- AS-ABS<ESYN.UW<2.2.3)/WW(2.2.l).ESY(JS*N.l).UW<2;i.3)/-N(2.FDDIFF 98

11,1)) FDlFFim DC 60 K ■ 1,4 FDIFF101 DO 30 J ■ 1,2 FDIFF102 MJ ■ NM2*J FOIFF103 DJ ■ DYA(JS*MJ) FDIFF104

30

108

3*HU|j*i»t<j*H(i.jiKn FDirnoe IF (,NOT,AXIS) QO TO 40 FDirfl09 Q = 0*S*(H(2,3,K)-HI2lliK)) FClFFlin QO TO 50 FDIFFU1

40 0 » DJl*<H(2,3,K)*h(2,l,K)) FOIFFU? 90 HMKJ ■ WW(2,2#K>.0*L*(r(3,2,K)-F<l,2,K>)-OAS«(G(J,3,K),G(2<l,K))-FniFFlli

1Q*VIST«{AQ1X«(WW(S,?,K)-WW(?,2,K)>-AC2X*(WW(2.2»K>-KHI1;2,K))*A01YFDIFF114 2*<HW{2I3,K)-WW{2,?#K)).A02Y«(MW(2»2,,K)«WW(2»1»K))) FPlFFll^

60 CONTINUE FnlFFU6 DO 70 J • 1,2 FnlFFll? MJ • NH2«J FDIFFUP DJ ■ DYAJJS^MJ) FnlFFHV DO 70 I ■ 1,2 FDlFFlüf MI ■ MM2*l FnlFM2l DIi-F « HAL«(00VMU*(VSE(JS*MJ*l)«ASY<JS*HJ*l>«<G<I»l,J*i;6)-G(I, J*lFnlFF12? l,6n*YbE(JS*MJ)*ASY(JS*HJ>«(ri(I^liJ,«)-G<I,J,6)))«TRE0TH«(YSE(JS*MFnlFFlZ3 2J*1)*(U( l*l,J*l,5)-(J(I.J»li5)»*YSE<JS*Mj)*(G(Ul,J,5>-Gel.J,5)))>-FnlFf 12< 3HAb«0DVMu*<G<I*l,J*1.6).G(I*l,J,6>*G<I,J*l,6)-C(r,J,6>> FnlFF12^ CCi ■ ,2S*TRE0TM»(ESY(JS*MJ*l)*(F<l«l,J*l,5>«F<I>J*i,9)*r(I*l,J*l,FniFFlif6 17>*F(I.J*l,7))»ESY(JS*MJ)«(F<r*liJ.5)*F(I,J.^>*F(I*l,J,7)*F(I,Ji7)FnlFFl27 2)) FtllFFlgP CCÜ • -.2&«TRE0TM*{a(I*l,J«l,5>*B<l*l,J,5)*C(I,J*l|S)»GlI.J,5)J FD1FF129 DC 70 K • 5i7 FDIFF130 T*V ■ ,25*<T<I*liJ*liK-4)«T(I*liJ.K-4)»T(I#J*l,K«4)»TII',J.K-<») FPIFF131 DUS « HAS*(ESY(JS*MJ«l)«(WW(I*l,J*l,K)*WU(l,J*l,K))-ESY(jS*MJ)*(WFnlFF132 INU^liJ.KUWMI.J.K))) FDIFF133 DUSS ■ HAL«(WW(Ul.J*liK)-UW<I,J*liK)*WW(I*l.JiK»-LH(i;j.K)) FriFFia4 MPlIiJiK) ■ ,25*<WW(I*ltJ*l.K»*WH(I*liJiK)*UW(I.J»l,K)*JW(I,J,K))*FnlFFl35 lH»L*(F(l*l,J*l,K)-F(IiJ*l.K)*r(I»l.J»K).r<I».l»K>)*H*S«(a(!*l.J*l.KFnIFF136 2)»ü(l*l,J,K)*G(I,J^l,K)-G(I,J,K))"CCl«DirSS"CC2*D|FS-TAW«nlFF-0AK*FPIFF137 3DJ*(H<l*l,J*l,K)»M(!*l,J,K)*M(I,J*l,K)*M(l,J#K)) FDIFF 138

70 CONTINUE FPIFF139 DO 100 K ■ 5,7 FnlFF14P IF (,NOT,AXIS) GO TO 80 FDIFF141 0 = 0ASMH(2,3,K).H(2aiK)> FniFF142 GC TO 90 FnirF143

80 0 = DJl*<H(2,3,K)«H(2iliK)) FP1FF144 90 HMK) ■ WW(2,2,K)*0»L*<r(3.2.K).F<l#2,K)»(W{HfJ,2> FnlFF145

1-ASY(JS*N)«W<HN|3)) w(HM<3#2,K)v.HM(l,2,K))-T{2,?.K-4)*YSFDlFF146 2E(JS»N)«(ASY(JS*N;.o0VMU»{Q»,t,?,6>-O(l,2,b))-TRE0Th«(8(3.?i^)-G<l.FPIFF14 7 32iS>)))*aAS»(G{2»3 K.-'-SC 1, ••w(i;".3)*(E8Y(j3»N*l)* FDlFfl^e 4HW(2i3|K)-ESY(.iS*N- ■')*WW(2I1.K))*T(2,>.,KV4)«(W(MN*N1P2,?) FDIFF 149 5.WlMN.NIP2>2)))-0*VlSr*(A01X«(WH<3,2#K).WU(2,2,K))-«QSX«(WW(2 FDIFF15Ü 6»2.K)"WW(l,2.K))*A0lfMHW(2,3.K)-WW(2,2iK))-A'52Y**WM2,?,K).HW{2,lFDIFFlbl 7,K))) FPIFFIS?

100 CONTINUE FDlFFISi DO 110 J • 1,2 FPIFFIS* MJ » NM2«J FDIFF155 A« ■ •ASYA<JS*MJ) FD1FF156 YStJ « YSEA(JS*MJ) FnirF157 ESYJ ■ ESYA{JS*MJ> FDIFF15fc DC 110 1 • 1,2 FP1FF15? R*.U • NP<I.J,1)«ESYJ FDIFF160 U » WP<IiJ.2)/WP(l,J,l) FPIFF161 V » MP(I,J,3)/HP(I,J.l) FDIFF168 E » MP(I,J,4)/WP(I,J,1)-0.5«(U*U*V*V) FnlFFl63

109

r

SU ■ wP(l,J,5)*ESYJ Sli ■ WP(1,J,6>«ESYJ S2<i ■ hPU»Ji7)*lSYJ P » PRS(RHO,E)

s WPlI»Ji4)«ESYJ

110

120 130

• Jil)

|J|4) iJi») • Ji6>

ij.l) • J>2) • J.ä) |J|4) • Jid>

ij.n iJii) • J«2)

• J«4>

»Jft»)

• Jin • Jii) • JiiO

T(liJ.3) CCNTJNOE DC 140 K IF (,N0T, Q * QAbM QC TO 130 0 « DJ2*( HN(K) ■ M

WP(1,J,2»**R»WP(1,J#3) r(l.Jil)«U-VSEJ«(Sll-P*AB«Sl2) r( J,J,1)*V*Y,5EJ*((P-822)*A''-S1?) YSEJ*<(E^P)«<U*AR*V)"S12«(V**R»U>-S11«U TwTDMJ.(2l«U-AR«V;«Y9EJ MU»(U**R*V)«YSEJ TwTDMJttJ.^AR^V-lD^YSEJ RHO«V H(I>J>1)*Ü«S12 H(I,Jil)«V-2t*S22-Sll (E*P-S2?»*V-ii*S12 TMTDMU'V 0, Wd.J.S) HC, J.l) H{l,Ji2) H(I.J.3)*P*S11*S2^ H(I,J|4) -TWTDHi)«V KU*U FRTDMJ»V 512 •.5*(Sll*S22) •S12

1.4 X1S> CO Tn 120 (2,2,K).H(2.1.K)*H(1.2iK).^(l<l,K))

(2,2.K)*H(2.1tK)*H(l,2,K)*H(l.l.K)) (K)-0*L*(FC2,2,K).r(l,2»K)*F(2,l#K>> K)*G{1.2,K)-G(l,l,f))-Q

F(I; l.K)«Q(2.1

140 CONTINUE DUF « HAL*(O0VMJ*(YSEA(JS4N)*ASYA(JS*K)*(G(2*2i6)

lJS*N.i)*ASYAUS*N-H«(G(2.1.6)-0(lil,6)n-TRCOTM«| 22ia)»G<li2,9>>*YSEA(JS*N-l)»(Q(2.1.5)«G<1.1.5>)»)» 3JS*N)*(G(Z,2,6)*G(l,2,6))»YSEACJS«N.l)«(G(2,l,6)*G

CCl ■ l25«TRE0TM«(tSY*(JS*N)»(r<2.2,5)*F(1.2,5)*FJ l»E!>YA<JS«N-l)«(F(2.1.5)»r(l,1.5)*F(2»1.7)»F<1.1.7>

CC<! ■ -.25«TRE0TM.(fi{2,2,5)»rJ(2.1»5WG(l,2,5)*G<li 00 170 K • 5,7 T*V • ,2!»MT(2.2.K-4)«T<1.2,K-4>»T(2.1»K-4)*T(l,li DUS ■ OAS*(ESYA(JS*N>*(MP(2>2,K)«HP(1«2,K))-ESYA(

1K>*HP(1.1IK))) PUSS ■ UAU«(WP(2,2.K)-UP(l,2.K)^WP(2.1.K)-WP(l,l, IF (.NOT,AXIS) GO Tfl 150 Q - ÖAb*(H(2,2,K)>H(2.1.K)*H(l,2iK).^(l.llK)) GO TO 16Ü

190 Q * DJ2MH(2.2|K)*H(2.1.K)*H{1.2IK)«H(1I1IK)) 160 HMK) a wN<K)*CAL*(F(2l2,K).r(l,2,K)*F(2,l,K)-F<l',

l,K)-G(2,i.K)*G<l,2,K)-G(l,l,Kn-CCl*LIfSS-CC2«DlFS

FOI •F164 FDl 'F165 Fni ■F166 FDl ■F167 Fni •F16P Fni •F16V FDl 'F170 FP1 ■F171

•AP*S22*V) FU1 ■ri72 Ft) I ■F173 Fni 'f 17* FDl ■fm Fni ■H76 FDl ■H77 Fni ■F17ti FDl •F17« Fni -Finn FDl ■Fiei Fni ■ua2 Fni ■Fl«3 FDl -Fie4 FDl ■Fie^ FPl ■nee FDl ■Flb7 FDI ■FIB« Fni rFlB9 Fni ■F190 FDI -F1V1 FDl ■F192 Fni ■F193 Fni -F194 FDI -F195 FDl ■H96 Fni -F197 FDl ■H98

LKHIOAS* (G(2.?FnI 'f 199 Fni ■F200 FDl ■F201

•G(1I?«6)) ♦YSEAtFDl •F202 YSEA(JS*K) •<0<2.FC1 ■F203 H*S*00VHU* (YSEACFDl ■F204 (1,1.6))) FDl -F20b 2.2.7)*F(l ,2.7))FD1 -F206

n FDI •F207 1.5)) F 'I ■F208

FDI "► 209 K-4)) KOI ■F210 JS*N-1)«(WP(2.1.FD1 ■»211

FDI •F212 K)) FDI "F213

Fni ^214 FDI "f 219 FDl rF216 FDl -f217

1,K))»0*S* (G(2.2F0I ^218 •TAy*0lFF- C FDl 'F219

110

r

170 CONTINUE FDlFf220 WtMN -?,1) ■ WN<l)«E8r(JS*N> Fnir»?2i W<HN -?,2) ■ UN(2)/HN(1) FnirF?2? W<MN -2,3) ■ MN(3)/MN(1> FDIFF223 VEu ■ t<(MN-2,2)«*2*y(HN-2.3)««2 FD1FF?2< W(MN -?(4) ■ AMAXl(HN<4)/WN<l)-0.5«VELiO,0) Fnm225 W(rtN -?,9) ■ WN(9)«6SVN FnirF226 M(MN .?,6) ■ WN(6)#EIVN FniFf?27 WtMN -?,7) ■ Wig{7)*i»YN „ FD FfJ^J YlbLD ■ H(MN-2,5)«*?*W MN.2.^)«#2«M(KN.2,«)*«2*W(HN.2,5)«W(MK.2,7)Fn FF22« IF (VIbLU.LT.YO 00 TO 200 FDIFF23(] IF (AXIS) 60 TO 1«0 FniFf?31 WCüT • ((«(MN.5>»*SV(JS*H)«U(HN.6))*<W(HN«1,2>-U<MN.1I2I)*<W<MN,6)FD1FF?32

l-Ab¥(jS*N)«W(MN,7)).(W<MN-ii,3)-H(MN-j,3)>)«0AL*ESV(jS»NI«(U(f'N,6)*FnlFF2JJ ^(^llMN♦N^p2,^)-w(HN-MIP2,^))•^|<MN»7)*(w(H^>^^IP2,3).w(H^.MIp2,3))•o*FnIFf ?34 3S«HAKMW(MN,5)«w(MN,7))«H(MN,3)«DVU8«N)> FPIFF?3'5

GC TO X9Ü FDlFf?3t 180 WCUT » U(MN,5)«((w<HN*l,2)-W(MN-li2)>«0*L-ESV(jS*K)«(k('lfUMF2i3)-FniFf ?37

lM<riN-NIP2i3))*0AS) FDlFf23e! 190 HCUTi*M*Xl(HDOT.0.0» rnIFF?39

ACUN » WDOT»MU/VC rniFF24n SSU ■ JW(MN-2,5>«AC0N«W(Mtg#'»))««2*(U(MN-2,7)-AC0N*W(Hk,7))«*2*(W(Mrnirf 241

lN-^»6J-ACON«H(MN,6>»**2*(W(MH-2i5)-AC0N*W(MN,5))«<Wm.2,7).AC0N*wFniFF242 2(^N,7)) FniFf243

ALHHA ■ SQRT(VC/SS0) FniFf?44 H(MM-2»5) ■ ALPHA«(U(MN-2.5»-AC0N«W(HN,5)) FnirF24,3 H(MN»2|A) « ALPHA*(U(MN-2,6J-AC0N«H<PN,*)) FnlFF246 W(MN.2»7) ■ ALPHA«(U(MN-2I7)-AC0N*H(PN,7)) FniFF247

200 PCbR ■ .THUE. FniFF24f RHU ■ W(MN-2,1) FnlFF249 E » MMN-2,4) FDIFF2&0 P « PBSCHHO.E) FDirF251 C2 ■ PH*P*PE/RhO**2 FD1FF?!>? IF (02,06.0,0» 00 TO 240 F0IFF253 WRITE (6,300) MM2,N,MAT,ESY{JS*N)IAKT,(W(MN-2,K)»K • l.KMAX) FDIFF2i)4 GC TO 230 F3IFF25!>

210 IF (NEIBH,UT.240) GO TO 230 FDJFFPbft L(MN) ■ 2 FDIFF257 DO 220 K ■ l.KPAX F01Ff?56

220 W(MN.2|K) » W(I"^,K) FniFF25<' GC TO 260 FOIFf260

230 BSAVE ■ B FDIFF261 C*LU ONESTP (M#N) FDIFF262 B = BSAVE FD1FF263 GC TO 260 F'51FF264

2«0 C » S0RT(C2) fDIFF26!) UC ■ (ABS(U(HN-2«2)-ASY(JS«N)*W(HN-2f3))*FIGr(jS*r.')*C)*DAX FniFF?66 VC ■ (ABS(H(MN-2,3))*C)«ESY(JS*N)«D*Y FnlFF267 SB « AMAXKUC.VC) F')IFF26fi IF (SB.LE.SBM) 00 TO 250 FniFF269 SBM ■ SB FniFF270 ISd ■ MM2 F01FF271 JSB • N FDIFF272

250 CONTINUE FOJrF273 BS • AK*SB FDIFF274 IF (BS.QE«0.9) WRITF (6.290) MM2.N,AKT.BS.MAT,(H(MN.2.K) ,K«1,KMAX)FP1FF27?

Ill

MUH

IF (BS.r.b.l.O) GO TO 230 260 CONTINUE

DC 270 M ■ l.Nj JJ»lJS»(N-l)«NIP2 DO 270 M • l.NI HK*JJ*H lim) ■ U(MN*2)

270 CONTJNUE DO 280 M • 2,NIM1

280 L<IJ8*M) ■ L11JS^?«NIP2*M) rf*T(22.M*T) ■ CFL/SRH IM*T(«,M»T) ■ 1SB IKAT(9|MAT) ■ JSB RE I URN

FDirF276 FniFF277 FnlFF278 FnlFF279 FnlFF2H0 FDIFF281 F01FF28Ü FDlFf?«^ FnIFF?ö4 FP1FF2«,5 FnlFF?«6 Fnm?H7 FniFf?Bfl FDIFF28« FnlFF2V(l

290 rCHHAT U1H *T PO.NT (I..lH.12.16H, IN OIFFP *T T,FO .,.,X,HST*B.r9FDIFF^

l,5.5X4MMAT»l2/aH W»7El5.5» .„,,«., TM^riNiPY SOUND SPEfC 1^ FD1FDIFF?93 300 FOKH*T (UH AT POINT «p'l«'^'1"»3^' i^Ji^g 5? FD1FF294 irFJ){4HHAT»12,3x4Hesv»F-9,».3X2HTir9,5/3H W«7ElJ.5> FPIFF29'.

EMJ

112

»■ v«ty

SlbROUTINE ONESTP <!I.JJ) ONtSTP d COMMON// U(2200.7),L(2200) 1NIV*c I COMMON/BNDCRS/ HB! (109,8,7),PBI (10«,a»# INDa09.9)i ?N„Huc T 1WBJ(78I8|7>,PBJ(7«.H>IJND<78,9) BNUCPS 3 COMMON/MSMrCN/ Y<78).DV<78).DYA(7«),E8Y(7«).YSE<7B),ESY*(78), MSMFCN d lYSb»<7»)#ESYE(78),ElQF(7«J»#»8Y(7e»l«YY(7e),ASYA(78> "

ST^O I

COMMON /MATARR/ NMAT. IM»,(ia,§).rMAT(23,5».«AT "llf"" ^ COMMON /COMVAL/ KT,»KT,nT.OTHIN,ITER,NEIPR,IPniNT,E«R.EPS.EPSl,RDlCnMVAL 2 lS|IOP,DAl.,KMAX,P0RC,P8CU.LP,Lr «E0?V^,L I COMMON /MATVAL/ AX,AY.CrL.Vl8.VIST,MU,YC,RH0,XO,PO,T0.XZ.A,B.ABL,DMATvAL 2 lABL,CHAN,BMAX,rACT,ANO,AF,SRH,AL.AS,AKlMAL,HA3,HA«,OAL,OA«!,'3AK,OAXMATVAL i 2,D*V#H0AX.HDAY,DAX2,DAY2.HDAXY,0DAXY,DTR»HALFMU.TWTrMU,rRTCMU,00VMMATVAU * SU.IREOTM.Nl.NJ.NFMAX.IS.JS.IJS.IBS.ISB.JSB.NIMi.NJMl.VDlNDl.NE.NElMATvAL b 4,N>,NIP2,NTR "*JVAL o COMMON /PRESS/ POER.PRiPE.MATNO „ ^!;D,n COMMON /i)ERl/ RT,UT,VT#ET.S11T,812T,S22T 2

N^IDJ,

COMMON /UER2/ RTT.UTT,VTT.ETT.S11TT,S12TT,S22TT OVfcSTPll DIMENSION WW(7), WT(7), HTT(7) S"";^, DIMENSION HSA(7)# WSB<7), WSAA(7), WSBB«7), WSAB<7) S^SIDH gCUlVAUENCE (RT.-Td)), (RTT^WTTd)) 0NfcSTP14 REAL KX.K2 S^ITPIä LOblCAL AXIS 0\bSTP16

REAL MU.MUMMS.MUPHS n^llPlfl

I J » JJ 0NfcSTP22 IJ»IJS»(J-1)«NIP2*I S^ITL^

AXIS ■ FALSE ONtSTP25 IF (J.60.2) AXIS - .TRUE. D^TP?7 AI - FL0AT(I.3).AX mtlVpll AJ - FL0AT(J.2).AY ntl74l DJ ■ ESY(JS*J)»OY(jq*J) n^cTP^O DO 10 KK ■ l.KMAX „ ^CTD.I Hta(KK) » WUJ.KK) S^^TO,'

10 CONTINUE O^STP3< 1 PCbR » .TRUE. 0NfcSTP33 PP • PHS(WW(l),W^(4)) SN^3o^ PPH i PR 0NfcSTP35 JJ^ J ll 0NfcSTP36 JPUIN^ » NE1BR/16 n^cTP^H IPOINT ' NEIBfl-16«JP0INT^l ONL?TP3« iPilThiT a JPnTNT*1 ONtS""^" GO to «20.40,20.«0,120,80.120.60,20,40,20.40,120,80.ISOieo). IPO INONtSTP40

lT 0Nt:STP41 C USX IS U SUB X UXX IS U SUB XX UXY IS U SUB XY ON»:STP4Z C USY IS U SUB Y UYY IS U SUB YY 2^!!-!? C UT IS U SUB T UXT IS U SUB XT UYT IS U SUB YT UTT IS U SUB TT 0^tSTP44 C SECTION 100 IS FOR WHEN NEIT"FR (IP,J) NCR <IH,J) IS MlSSlKG S^H^J! _ 0NLSTP4O

20 DO 30 KK ■ l,KMAX S^IIPI« HSA(KK) ■ <W(lj*l,KK)-W(IJ-l,KK))«HDAX SI^ETOIQ HSAA(KK) ■ (W<IJ»1,KK)-2.0*WW(KK>*W(IJ-1,KK))*DAX2 0NfcSTP49

30 CONTINUE ONtSTPbO

113

• ■«.

■ .-.^

•

PJ ■ PHS«W(IJ*1,1),U<IJ*1,4)) pfil • PR

PEX • PE P2 ■ PHS<*(IJ-1,1),U(1J-1,4)) PR^ » PR PEü • PE PSA ■ (Pi-P2)»H0AX PRSA « IPR1-PR2)»MD*X PEäA ■ (Ptl-pEj)*HD»X PAA ■ (Pl-2,0*PP*P2)*D**2 DELX ■ AX GC TQ 16Ü

40 N s JND<JS*J,1) UC 50 K « 2iN If «AI,Lfc,PBJ(jS*J,K)) r.O TO AO

50 CONTINUE 60 Kl ■ PbJ(JS*J,K)-*l

K2 ■ AX IF (K1,LT,RDIS«AX) (10 TO 680 DELX ■ Kl DK » 1,/(K1«K2*<K1»K2)) SKI ■ DK*K1**2 SK^ ■ UK*K2**2 Kl » 2,*Kl«nK K2 = 2,*K?«nK DC 70 KK ■ l.KMAX WSA(RK) » SK2*<WBJ(JS*J.K,KK>-WU(KK>)«SK1*(WW(KK).W(1J-J.KK)) HSAA(KK) » K2*(WBJ(JS*J,K,KK)-HH(KK))-K1«(WW(KK)-W(1J-1;KK))

70 CONTINUE PI ■ P«S(WSJ(JS»J.K.1).UBJ(JS*J.K,4))-PP PHI ■ PR.PPR PE1 ■ PE-PPE P2 ■ PP-PHS(W(IJ»1,1),W(IJ-1,4)) PR*; ■ PPH-PR PE^ • PPE-PE PSA ■ SK2«P1*SK1»P2 PfiSA i SK2*PRl«SKi*PR2 PEbA ■ SK2*PEl«SKl*PE2 PAA ■ K2«P1-K1*P2 GO TO X6u

80 N » JNU(JS*J,1) DC 90 K ■ 2.N IF (*I,LfciPBj(jS»J,K)) RO TO 100

90 CONTINUE 100 Kl ■ PöJ(JS*JiK)-Al

K2 ■ Al-PBJUSO.K-D IF (KliLT,RDIS«AX10R.K2.LT.Rr!S*AX) RO TP 68C DEUX » AMlNl(KllK2) DK • K1*K2 SKI • K1/(K2*DK) SKÜ > K2/<K1«DK) Kl ■ 2,0/(Kl*DK) K2 • 2,D/(K2*DK) DO 110 KK ■ liKMAX HSA(KK) » SK2*(W9j(jS*J,K.KK)-HW(KK))*SKl«(WW(KK).WflJ(JS*J.f.

1)

0MbSTP51 ONtSTP52

ONhSTPSi 0NfcSTP54

ONbSTPSb 0NtSTP56 ONtSTP&7

OMtSTPbfl ONtSTPb? 0Nt?TP6'l 0NfcSTP6l ONtSTPft^ ONfcSTPftJ ONtSTPb« 0NfcSTP65 0NtSTP6ft 0NkSTP67 0NtSTP68

0NtSTP69 ONfcSTP7n 0NfcSTP71 ONtSTP72 OMfcSTP73 ONfcSTP74 ONfcPTP7e' 0NtSTP76 ONESTP77 0NtSTP78

0NtSTP79 ONfcSTP80 ONbSTPBl 0NtSTPa2 0MtSTPfl3 OMfcSTPBA 0Nt;STP85 0MtSTP86 0NfcSTP87 0NbSTP88 0NbSTP89 0NbSTP9Ü ONfe<;TP91 0NfaSTP9? ONbSTP93 0NbSTP94 ONbSTP95) ONbSTP96 0NbSTP97 0NbSTP98 0NbSTP99 ONbSTlOO

ONbSTlOl ONtST102 OMtST103 OMbST104

l,KK)OMbST10!> ONbST106

114

llü WSAMKK) ■ Kl*(W3j(jS*J.K,KK)'HU(KK))aK2*(WU(KK)"WBj(jS«J.K Pl • PRS(WBJ(JS*J.K,1)|HBJ<JS*JIKI4))-PP Pfil • PR«PPR PE1 • PE-PPF P2 ■ PP-PRS<WBj(JS*J,K-l,i>."BJU$*J,K»l,4)) PR«: • PPR-PR PEü » PPfc-PE PSA ■ SKa,Pl*SKl»P2 Pfib* » SK2«PRl»SKl««»R2 PEbA « SK2«PE1*SK1«PE2 PAA ■ K2»P1-K1«P2 GC TQ 160

120 N s JNÜ(JS*J,1) DO UO K ■ 2,N IF {»I,LT.PBJ(JS*JiKn GO TO 140

130 CCIMTINUE 140 K s K-l

K2 • AI-PdJ(jS*J,K) Kl > AX IF (K2ILT.RDIS«AX) RO TO 680 UELX a K2 DK i l,/(Kl«K2*(<l*K2)) SKI ■ UK«K1««2 SKi ■ UK«K2**2 Kl » 2,*Kl*0K K2 » 2,*K2*DK DC ISO KK ■ liKMAV MSA(KK) > SK2*(U(IJ*1.KK).UW()<K))*SK1*(MU(KK)-MBJ(JS-*JIK.KK rtSA*(KK) « K2*(W(IJ*1,KK>-WU(KK»)-K1«(HN(KK)-WBJ(JS*JIK'.KK)

150 CONTINUE Pl » PRS»U(IJ*1,1),W(IJ*1,4)).PP PRl ■ PR-PPR PEl i PE-PPE P2 « PP-PRS<Kt1j(JS*JiK,l),WRj(JS*J#K#4>)

Pfiü i PPR-PR PE2 » PPE-PE PSA ■ bK2*PJ,*SKl*P2 PRbA a ^Ki*PRl*S«l*PR2 PEbA ■ SK2*PEl*SKi*PE2 PAA ■ K2»Pl-Kl*P2

160 GO TO «170,170,19n,l90#l70»l70,190,HO,230,230,270,?70,230, 1,2/0), IPOINT

170 DC 180 KK « l,KMAx HSB(KK) n (W(Ij*NIP?,KK»-W(IJ.NIP2,KK))*HnAY WSdB(KK) ■ (W(IJ»NlP2,KK)-2,C*HW(KK)*W(IJ-NIP2,KK»)«n*Y?

180 CONTINUE Pl « P«S(W(1J*MIP?,1),W<IJ*NIP2,4)) PRl ■ PR PE1 ■ PE P2 » PHS(W(IJ-NIP2,1),W(IJ-NIP2,4>) PR«: ■ PR PEü ■ PE PSb ■ <P1-P2)*HDAY PRbB » (PRl-PR2)»HDAY PEbB « (PEl-pE2)*HDAY P8b ■ (P1"2,0*PP*P2)*DAV2

-l,KK))ONtST107

ONtSTlOH ONtSTlC ONtSTlin ONbSTlll ONfcST112 0NfcST113 ONtSTll« ONtSTllb ONtSTll^ ONtST117 ONfcSTll" OMfcSTll« 0MfcST12C 0NtST121 0nfc?T12i: O'JtSTli^ ÜMtSTl24 0NtST12'3 0NfcPT12'i 0.ltST127 0MtSTl2fl 0NbSTi2V OMtsTian 0-gfcST131 0MbST132 0NtST133

)) 0NtST134 ) 0NbST13^

0^bST136 ü'jbST137 0MbST13fl ONbST139 0NbSTl4T ONbSTl43 0NbST142 0Sb«;T143 0»JLST144 O'JbSTi^t) 0NbST146

?3C,2700MfcST147 0hbST14b OMbSTl49 O^bSTlSP ONbSTlST ONb<;Tlb2 OMbSTlS; ON'bSTlS« OMbSTlbS 0MbST156 0NbST157 ONbSTlbe 0^bSTl!>9 ONbSTl60 0NbST161 0NbST162

115

ÜELV - *y 0NtST163

190 N » 1NU(IS*IM2,1) lllliill DC 200 K • J.N ^CTJ*7

200 CCNT1NUE TJtVy\il 210 Kl • PJinSMH2.K,.M ^S1169

IF <Kl,LT.RDIS**r> r.o TO 6Sn SüuH^i

sKiY. ü!iKi..2 j;;^;7;; SK,; ■ BK«K2..2 0NMTO6

KZ - 2,.K2.DK §NfclTi7P ÜC 220 KK ■ l.KMÄX ONfcSTIZH WSd<KK) • SK2MW9l(fS»IM2.K<KK)-WH(Kn)*SKl*|llW(KK).WlIJ-f'lP2.KKn0NtSTl79 wsSö(KK) - l<2.(Wai<iS»IH2.K.KK)-HMKK)>.Kl.<WW(KK>.W(U.MlP?,NK)) ONtSTIBÜ

220 CCNTJNUE ONtST181 Pl » PHSJ«3I<IS*IM2.K,1),WB1(IS*IM2,K.4))-PP n^cTi^i PB1 ■ PR.PPR ^UCTJ«4 PEl • PE-PPE OMtSTlö« P2 • PP-PHS(W{IJ-NIP2.1>.W(1.).NIP2.<)) ETJBA

P^ ' PPH"PR mtlVll* p^ ■ ppfc-pE ZtlAll PSd • SK2*P1*SK1»P2 ^fcqTifl9 PRbö . SK2*PR1*SK1.PR2 „.,ucTion PEb9 . SK2.PE1»SK1.PE2 2^ST191 PBb . R2.P1-K1.PZ SuSTl'z

230 N ' 1ND(|S*IM2.1) IIIIAIA DC 240 K • 1,N ZclAVb IF UJ.LT.PBKISMM?,«)) CO Tn 250 Zllrill

2.0 CONTINUE g-ST19.

Jf ". ^-pBI{Is*,k1^•,', Ztlnl* IF <K2,LT.RDIS.AY) GO TO ABO TulVrlll ^ ' 1./«K1.K2.(K1*K2)) ITtlViV?

DC260KK11KMAX u«Nca i eu f WSU(KK) ■ SK2MW(lJ«NIP?,KK)-WM{KK))*SKl»(HH(KK>.WBI(IS*lM2.K.KK))ONfcST20fl WSdBCKK! - K2MW(ij^IP2.KK>.HH(KK)>.Kl*{WH(KK)-H«I(!S*|H?,K,KK>) OVfcST209

260 CONTINUE ZlllAl Pl ■ PRS(W(IJ*NIP2,1).W(1J^NIP2,4)>-PP n^cT9i5 PRl • PR-PPR ^tVrlll PEl ■ F*E«PPE ONfcSTZlJ P2 • PP-PRS(WPI(IS»!M2,K,l>.MflI<IS*IKZ,K,4)) S^CT^Ü

;ii: Zl-X ; PSb ■ bK2*Pl*SKl*P2 muplraifl PRbB « SK2*PR1*SK1«PR2 ONtSTZJä

116

■■*i '••;y

PEbB ■ S|<2*PE1*SK1*PE2 PBH ■ K2«Pl.Kl.f»2 GC TO HO

270 N » IN0(1S»IM2,}> 00 260 K ■ 1,N IF <AJ,Lt,PBmS»lM>.K)J 00 TO 290

280 CONTINUE 290 Kl ■ PB1(IS*IM2,K)-*J

If (K1,LT,RDIS**Y) nO TO 680 If U.t0.2) GO TO 310 K2 ■ *J-PB1(IS»IH2,K-1) IF (K2,LT,RDIS«*Y> 10 TO 680 UELY » *MIN1(K1,K?> DK ■ 1,/(K1«K2«(K1»K2)) SKi ■ 0K*Kx**2

Kl ■ ?,*t<l*DK K2 • 2,*K2«DK 00 300 KK ■ l,KM*x WSU(KK) ■ SK2*(WBI(|S*IM2,K,l<'K)-HU(KK))*SKl«(WH(KK).WflI

i.KKJ ) HSÖ8(KK) • K2«(HBI<TS*IH2,K,KK)-HH<KK)).Kl«<UW(KK>-taBI(

1KK)> 300 CONTINUE

PI ■ PHS(WBt<IS*lH2.K,l>.WBl(IS*IH2iK.4))-PP PR1 a PR«PPR PE1 ■ PE-PPE P2 ■ PP-P''S(hBl<IS^|M2,K.i#i).WBI<IS*IH2,K-l,4)) Pfl<f • PPR-PR PE«! • PPfc-PE PSb ■ SK2*Pt*SKl*P2 PfibB ■ SK2«PRl»SKi«PR2 PESB » SK2«PE1*SK1*PE2 PBd • K2tPl-Kl*P2 GO TO 430

310 WSö(l) « 0. HSd(2> * 0. HSb(3) ■ WBI(IS*IH2.K.3)*DAV/K1 OELY ■ Kl SKI ■ 2.0/(Kl*Kl) DO 320 KK ■ l.KHAx HSUB(KK) ■ (HBI(IS*IM2,K,KK)-WH(KK))»SK1

320 CONTINUE PSd «0.0 PRäB ■ 0, PESB . 0. PBb ■ (PHS(WBI(IS*IM2.K,1)#MPI(IS*IM2,K,4>)-PP>»SK1

330 PDfcR « .FALSE, GO TO (540,360,400,360,340,420,400,480,380,380,440,920,

1,600), JPOINT 340 00 390 KK ■ 1,KMAX

MSAB(KK> ■ ((W(IJ*NIP2*1,KK)-W(IJ«N1P2«1,KK))*HDAK-WSA{ 390 CONTINUE

PI ■ PHS(W(IJ*NIP2*1,1),W(IJ*NIP2*1,4)) P2 ■ PHS(W<IJ»MIP2-1,1),W(IJ*NIP2-1,4)) PAd ■ l(Pl-P2)*HDAX-PSAJ*DAY

0NfcST2i9 OgbST?20 0NbST221 0NkST222 0NbST?23 0NbST22l 0NbST?2!) 0NbST226 0MbST227 0NbST2^o 0NbST2?9 0VbST2JU 0NLST231 0NbST23? 0MbST?33 0MbST234 0MbST23b 0NfcST?36 0NbST237

«!S*IM?,K«i0NfcST2Jfl 0NbST239

»'5*IK2.K-l,0NbsT24U 0MbST241 0NbST?42 0NbST243 0MbST244 0l>ibST245 0NbST24A 0NbST247 0MbST248 0NfcST249 ONtST260 0MbST261 0NbST252 0NbST253 0MEST254 0MfcST255 0\bST256 0NbST257 0\b«?T268 0^bST^59 ONbST260 0NbST26l 0«JbST262 0NbST263 0NbST264 0MbST265 0NbST266

34n,50C,«60ONbST267 0NbST268 ONbST269

KK))*CAY 0»!bST270 OMfcST271 0NbST272 0,JbST273 ONbST274

117

ONtST27b CiC TO S60 0MbST27ft

360^BUKr."(iisK;;;,.(W«.J.N.P^l.KK,-W(tJ..:P2-i.«K,).H0AX>-D*r 0^77

370 CCNTJNUE ....-^ ..,, 0NtST279

P2 « PHS(W<IJ-NlP2-l.l>.wnJ-NlP2-1.4)) 0NfcST2Bl P»b ■ JPS*-<P1-P2>*M0AX)*DAV 0NtST?B2 UO Tu 1>60 0NtST2ö3

380 DC 3»0 KK ■ i.KMiy wies.i.KK)»•HQAY)»DAX ONkST2B< HSABtKR) ■ <WSB(KK)-(W<IJ*NIP?-1#KK>-W(IJ-NIP2-1.KK)MMD*YJ«C»« 0(lJtsT2öb

39U CCNTINüF. dti „,_, , ... 0NfcST2B6 PI • PHS(«(IJ*NlP2-l,l).wnj*MIP2-l.j ONtST?B7 P2 ■ PRS{K<IJ-N!P2-1.1>.W«IJ-IJIP2-1.4)) ONbST2Bfl P»b ■ <PSb-(Pl.P2)*WD*V)«DAX 0NtST2B9 GC TO 960 0NtST29(i

410 CONTINUE , . ... 0NfcST293 Pi ■ PRS(W(IJ*N1P2»1.1).W(IJ*MIP2*1.4) 0NfcST294 P2 • PHS(W(IJ-NIP?*1.1>.W(1J-NIP2*1,4)) 0^bST295 PAb ■ KPl-P2)*W0AY-PSB)*nAX 0NkST296 00 TO »60 0NtST297

420 OK ■ -HDAT*DAX ONt5T29H DO 430 K« « l.KMAX n#uu(K 0».ltST299

430 WSA8JKK) » (W<IJ-NlP2*l.KK)*fCIJ*NlP8-l.KK>-2.0*Viy(K ONtFT30n lK)-AX*AX«WSAA(KK)-Ar«AY»WSBn(KK))*DK ONbST301

PI • PRS(-(IJ-NlP?*l.l).wnj-NjP2*}'i OMtST302 P2 « PHS(MIJ*NlP2-1.n.«nj4NlP2-1.4>) OMkST303 PAb • (Pl*P2-2.0*PP-AX«AX«PAA-AY«AV#PBB5.0K nNtST304

GO TO »60 ONtST305 440 DK ■ HOAY'DAX ONbST306

DC 4S0 KK ■ liKMAX n*uu(K OMbST307 450 HSABJKK) - (H(1J.NIP2»1.KK)*W(IJ-NlP2-l.KK)-2.0*WU (« 0^tST3ü8

1K)-AX*AX«WSAA<KK>.AY«AY.WSBB(KK))«DK ONbST309 PI > PRS(W(IJ*NIP?*1.1).W«IJ*NIP2*1.4 0NbST31ü P2 ■ PRS(W(IJ-NlP2-l.l>.wnj-NlP2-l,4n ONbST311 PAb • (P1»P2 '.0»PP.AX»AX*PAA-AV*AV*«'8e»*DK ONbST3l2 GC TO »60 ONbST3l3

460 DK ■ HUAY*DAX 0NbST3l4 DO 470 KK ■ liKMAX .o^*,,•»/«w>*WAy»L«Ai«KK)1 - 0NbST3X5 470 HSABIKK) » (W(IJ»MIP2*I.KK>-HW<KK)-AX«<WSA(KK)»HAX»USAA(KK)) 0NtST316

lAY.(KÖ<KK)»HAY»-SBB(KKn).nK .PP-iX. <PSA*HAXOMbST3l7 PAb« «PRS<W{IJ*NIP?*1»1).W(IJ*NIP2*1.4)) r 0NbST3ifi

l*PAA)-AY«tPSB*HAY«pRB)>*0K 0Nb5T319 GC TO »60 ONbST32l

480 DK ■ «HDAT'DAX 0NbST321 DO 490 KK ■ liKMAX uu(kK>-AX«(WSA(KK)♦HAX*HSAA(K0NbST322

490 HSAB(K«) ■ (H(IJ-NIP2 *l,KK)-WW(KK)-AX«iikSAir. n« 0MfcST323 tKJJ-AY.CWSBtKKj-HAY.WSBBtKKjjJ.OK ^-,4 ,5 .pp-AX.ONbST32* PAH • (PHS(W<IJ-NIP2 •1,1>,W(1J.MP2 !•" 0NbST325 1{PSA»HAX«PAA)*AY»(PSB-HAY«PBP)>*DK 0MbST3,26

GO TO »60 0NbST327 900 DK • -MOAY«D*X 0NbST32H

DO 510 KK • i.KMAX 1,lo-uu(KK>*AX«<WSA(KK)-H*X*WsAA(KK))-0NbST329 510 HSAB(KK) ■ (WtlJ»NlP2 -1, KK )-WW < KK ) «AX* (WSA« >v« > nn* s QNfcST33n

1AY«(WSB(KK)*HAY*<*SB0(KK))»«DK

118

tatiMI

P*ö • (PHS(W(|j*NIP9 -1.1>,M<IJ*NIP2 -li4>)-pP*AX*(PSA-HAX0NtST331 l«PAA).AY«(PSB*HAV*PnB))*DK 0MtST332

OC TO »60 0NtST333 520 D« • HD*yDAX ONtST3.54

DO 530 KK ■ l.KMAX 0Mt«;T3J'5 530 MSAB<KK) ■ (W(IJ-NIP2 -i.»<K>-WM<KK)*A)(«<M«AeKK).HAX«HSA*(K0NfcST336

tK))*AV*(USB(KK).HAy*HSBH(KK)))*DK ONtSTjj? PAU ■ (PHS(W(IJ>NIP3 -1,1),W(IJ.NJP2 -i;4))-P^«AX*0NfcST33fi

l(Pt>A-HAX*PAA)*AV*(PSB*HAY*PB(>))«DK ONbSTSS« GC TO »60 0NtST34n

540 DC SSO KK ■ l.KMAX 0NbST341 WSABCKK) ■ <W(IJ*Nl*2«l,KK)-V!(IJ*NIP2-l,KK)-W(IJ-MP2*i;KtO»Mt IJ-N0NfcST342

lIP^-l.RKjJtQDAXV 0VtST343 550 CONTINUE 0»ifcST344

PAd ■ (PHS(M<Ij*MtP> ♦1,1),W<IJ*MP2 •l,4))-Pt>S«H(lJ»'1lP2 0NtST34b 1 -lilliW(IJ*NIP2 -l,4))-PRS(H(IJ.KIP2 •liD.WdJ 0NtST346

-1.1).W(IJ-MP2 -lONtST347

0MtST349 ONtST3&0 0NtST351 0NfcST3Ö2 aNtST353 O'tSTSM 0MfcST355 0^fcST356

CvfcST358 0MfcST3!>9 0MfcST360 0NfcST361 ONi ST362 0Mfc3T363 0Ni;ST364 0NtST365 0NfcST366 0NfcST367 0NtST368 0NfcST36,J ONtST370 0NfcST371 0NbST372 ONbST373 0NbST374 0NbST375 0NbST376 0NBST377 0NbST37e 0NbST379 0NbST3H0 0NbST381 0NfeST3B2 0NbST363 ONEST3e4 0NbST385 0NbST386

119

2-MP2 ♦li4))*PRS(W(IJ-NlP2 3,4))). ÜDAXY

560 RR ■ MIH1) UU ■ UW(2) VV ■ WW(3) EE ■ WW(4) SU ■ MU(9) Slü • MW(6) S2* m MW(7) DR ■ 1 ,/RR TU ■ SU-PP T2^ • S22-PP RSA ■ HSA(l) USA ■ NSA(2) VSA ■ MSAO) ESA ■ hSA(4) SUA i WSA(5) Slü* • < USA(6) S2<!A i ' WSA(7) RSU ■ MSB(l) USU ■ HSB(2) VSö ■ MSÜ(3) ESü ■ wSb(4) SUB • WS8<5) SlüB • WSÖ16) S21S • WSÖ(7) RAA a MSAA(l) UAA ■ MSAA(2) VAA ■ MSAAtS) EAA ■ HSAA(4) SUAA ■ WSAA(S) SlüAA ■ WSAA(6) S2ÜAA ■ HSAA(7) RAU ■ HSA9(1) UAb ■ NSAB(2) VAB • MS*B(3> EAb ■ riSAB(4) SllAB ■ MSAB(5) S12AB ■ HSAB(6) srua ■ HSAB(7)

•n äSttä

HPö ■ NSHPd) UBd ■ MSUB(2) "Bö ■ MSUB(3) bSb ■ MSBU(4) SU8B ■ MSBBtS) SUB» • WSBB(6) S2^BB ■ WSBB(7) TU* ■ SUA-PSA T2ÜA ■ S22A-PSA TUB ■ SUB-PSB TitB • S22B-PSB TU** ■ Sll**-P** T2<f** • S22AA-PA* TU*B > SUAB-PAB T2^BB ■ S22BB-PBB ö » ESY(JS*J) ee ■ YSE(JS*JJ»DJ BSb ■ feSVE(JS*J) AP ■ ASY(JS«J> AVb ■ AYV<JS*J) MUHHS ■ HÜ*I9*(S11>W22) MUMHS ■ MU-,5*{S11-S22) UV • UU-AP«VV UV* ■ üSA'AP*VSA IF (AXIS) GO TO 5B0 ERHS « PP*S11*S22 HS* • ,5«(SUA«S22AJ HSti • ,9«(S11B-S22B) rAPl2 • FRT0MU-AP»S12 S1ZTWT » Sl2-TwTDMU«Af>

TW 112 ■ TWTDMU-AP«S12 S12FRT ■ S12-Ap«FRTnMt) UVH « USd-AP*VSB-AYF*VV UV** ■ UAA-AP*VAA UVAB ■ UAB-AP*VAB-AYE*VSA VI* ■ VSA*AP*USA STUV o 312*USB*T22*VSB STU • m-AP«Sl2 STV ■ S12»AP«T22 STUA • T11A»AP«S12A STVA s S12A-AP*T22A TS^PSl • 0J*<2,«S22*S11) SIP ■ TWTDMU«DJ*VV SIPA s TWTDMU*DJ*VSA SIHB « TWTDMU«DJ*(VSB-BB«VV) RBU ■ HR«VSB*VV*RSB U6Ü ■ VV«USB-DR*S12R VBU ■ VV«VSB-DR*T22R EAU ■ STU*USA«STV*VSA EBU ■ VV«ESB-DR*STUV SUBD • VV*SllB*Sl2*USB*TUTDnu*VSB S2i;BD • VV«S22B*Sl2»USB-FRTDHU«VSB RT ■ -HR«ÜVA-UV*RSA-B*RBD-RR*VV«DJ UT ■ .UV«USA*DR*«STII**DJ*S12)-B*UBC VT ■ -UV«VSA*DR«<STVA*TS2PSl>-B«VBD ET ■ -UV»£SA*DR*E*0-B*EflD-VV«OR«DJ*ERHS

ONtST387 OMkST38ö 0NEST3B9 GNfcST39n 0NkST391 0NkST392 0NbST393 ONhST39« 0NtST39i) 0NtST396 ONfcST397 0NtST39C 0NfcST399 ONtST400 ONkST401 ONtST40Z ONfcST403 OMtST404 OMfcST405 ONeST406 0NfcST4«7 ONtST408 OMEST409 ONtST410 0MtST4U 0NfcST412 0NfcST4l3 0NhST414 0Nt5T415 ONbST416 0MtST4l7 ONt3T418 0NbST4i9 ONtST420 ONbST421 0'gtST422 OMbST423 0NbST424 0NbST429 0MbST426 0NbST427 0NbST42B 0NbST429 OMbST430 0MbST431 0MbST432 0NbST433 0NEST434 0NbST435 ONbST436 ONbST437 0NbST43fl 0NbST439 ONbST440 0^bST441 0NEST442

120

■ti. f'.wia/

P7 • R7»pR»ET.pE SliT ■ -UV«8llA*r*Pl2«U8*-Sl2TMT«VSA-B«SllB0-SIP Sl^T ■ -UV*S12A*HIIPUS*VSA-AP«HUNHS*US*-B*<VV*S12B»HUHH S2«!T > -ÜV«S22A-TWT12*U8**S12PRT*VS*-B«S22BD-SIP UV I • 0T-AP*VT TUT ■ SilT-PT T2ÜT ■ S22T-PT HSI ■ ,9«(S11T.S22T» SIHT ■ TWTDMU*DJ»VT RAi ■ •RH*UVAA«2.*RSA*UVA-UV«PAA-a*(RR*VAB*RSA«VSB*VSA

1-CJ«(RH«VSA*VV«RSA) UAI ■ •ilVA«uSA«UV*UAA*DR*(TllAA-AMS12AA-RSA*nR*(!;Tl;A*

112A)-R*(VSA*USB*VV*IIAB-DR*(S12AB-0R*RSA*S12B)) VAI • -UVA«VSA-UV*VAA*D»*(Sl2AA-AP*T22AA-DR«PSA«(5TVA»

12,*S22A*SUA))-B*(VSA«VSB»VV«VAB»DB<»<S22AB-PAB-DP»RSA« b*i a -UVA*ESA>UV*EAA*DR*((T11A-AP«S12A)*USA*STU*UAA#(

l)*VSA*bTV*VAA>DR*RSl*EAD)>B«(VSA*ESR*VV*EAB-C''*(T22A*V 2l2A«uSd*S12*UAP-DR*RSA«STUV)>-DJ*DR«(ERHS«(VS*-DP«RSA* 3SUA»S22A)}

PA I ■ HAT*PR*RT*PRS/t*EAT*PF*r.T*PESA SUAT ■ •UVA*SilA.üV«SllAA*rAP12*UAA-S12TUT«VAA-Sl2A«V

lie*VVbU»B-Sl2A«lJSR-Sl2*UAB*THTDMU«VAB)-SlPA Sl^AT « •UVA«Sl2A.UV«Sl?AA*HSA*VS**HtPHS«VAA-Ap*(MUKH^

l>-d*(VaA«Sl2B*VV»Sl?AB*HSA«US0-MUMH9«UAB) S2<iAT • -UVA*S22A.UV«S22AA-TWTi2«UA»*Sl2FRT*VAA*St2A*V

12e*VVS22*B*Sl2A»US"»*Sl2*UAB-rRT0MU*VAB>-SlPA UVAT • L(AT-AP*V*T RBI ■ •RH«UVAB-RSR«UVA-UVB«PSA-UV«RAE-B*(PR«V9B*2;*9S<?

l-ebE»RBD-DJ*<RR*V<;9»VV*RSB-RP«RR«VV) UBI ■ •UVB*USA«UV*UAB*PR*(Tl].AB-AP*Si2A6>AYE*Sl2A*D0*R

1S1<!)»0J*(S12B-BB*S1?))-R«(VS'1»USB*VV»UBB-0R«(S12PR-CR» 2SE*UbD

VEI ■ -UVB«VSA-UV«V*B*DR«(S12*B-AP«<S22AB-PAB)«AYE*T22 lA*UJ»(2.«S22B*Si:B-(2.*S22*Sll)*flB)-CR«RSB«TS2PSl»-B«( 2BB-DR*(T22BB-DR*RSB*T22B))-RSE«VBD

EBI • -UVB«ESA-UV«EAB*DR*((T11B-AP«S12B»AVE*S12>*USA*? l-AH«T2<iB-AYE*T22)«V8A«STV«VAn-DR«RSB*EAD)-B*<VSB*ESB*V 22e*VSB*T22«VBB«S12B«USB*Sl2*MBB-DR*RSB«STllV>)-BSE«EBD. 3RMa*VV«(PSB*SliB»S2?B)-VV«ERHS*(DR«RSB*PE))

per ■ HRWR*RT«PRSR*EBT*PE*ET*PESB SUBT ■ -UVB«SllA.UV*SllAP*rAP12*UAB-Sl2TWT«VAB-S12B*V

lUS*-TWT0MU«VS*)-B*<\/SB«SllB*VV«SllBB«S12P«USD-S12«UflB* 2BSb*SllB0-S!PB

SUBT ■ •UVB*Si2A-UV*Sl2AB*HSR*VSA«HtPHS*VAB-AP*(MUMHS 1)-AVE«MUMHS«USA-B»{VSB«S12B*VV 12BB*HSR«USB«MUMHS«IBP 226-MUMHS«USB)

S2<iBT ■ •UVB«S22A-UV«S22AB-TUT12«UAB*S12rRT*VAB*S12B«V lUSA>rRTDMU*VSA}>S*(vSR*S22B*VV*S226B*S12P*USP*S12*UeR* 2BSb«S22aOaSIPR

RTI ■ -UVA*RT-RR*UVAT-RSA«UVT-UV*RAT-B«(f:R*VpURT«VSB* 1B>-DJ*<RR*VT*VV«RT)

UTI ■ -UVT«USA-UV*UAT*DR«(S11*T-PAT-AP*S12AT»RT*DR«(ST 1J*S>12T)-Ö«(VT«USB*VV«UBT-DR«{S12BT-0P*RT«S12B))

VT1 ■ -VSA*UVT-UV*VAT«DR*(S12AT-AP«(S22AT-PAT)-DR«RT*( 1«.DJ«(2,*S22T«.S11T)),B*<VT«VSB*VV*VBT-DR*(S22BT.PBT-BR«

ETI ■ -UVT«ESA.UV«f*T*DR*((TllT-AP«S12T)«USA*STU«UAT*(

ONfcST M3 ONkST M«

S»USB) 0McST Mb ONtST «46 ÜNfcST M7 O^itST Mb ONfcST M9 ONfcST ♦ 60 OMfcST «Öl

•RSP*VV*RAB)ONkST «62 ONfcST «53

sii*rj)»Dj«soNfcsT »•>< ONtST «5.6

TS2PSl)*DJ*tO-JfcST «66 T22P)) ONfcST »67 S12A-AP«T?2A0MfcST • 6« Sn*T22*VAP*S0vfcST »6? VV)»VV«(PSA*ONtST. 16(1

ONfcST 161 ONfcST' ib*

UA-PMVSA*SlONtST' 163 ONfcST' 16-»

• !!AA-HSA«IJSAONfcST' ib^ OMtST' 16(1

UA-P«(VSA*S?ONfcST' 167 ONfcST' 166 ONfcST' 169

•VSn«VV*RBB>ONEST< 170 ONfcST- 171

SR*<STtA»DJ*ONfcST' 172 RSB*Sl2P))-PONfcST' 173

ONtST' 174 A«DR«PSB«STVONtST. 175 VSB«VSB*VV*VONfcST' 176

ONfcST- 177 TU*UAB*(S12BOwfcST' I7P V*EpP-DR*<T20MtST' 179 Dj*DP*<VSB*EONtST' ten

ONtST< 61 ONtST' 1Ö2

UA-AYE«IS12*ONtST- 163 TUTrHU*VBB)-ONfcST' 164

OflfcST' 185 ♦JAP-HSP'USAONfcST' 86 )»B?F*(VV*SlONfcST' (87

ONfcST' (88 UA*AYF«(S12*0NtST' (89 FRTPMU^VBBJ-ONtST^ 90

ONtST' (91 VW*ReT-»VT*RSONtST< (92

ONfcST^ (93 UA*Sl2*DJ)*D0NtST' (9«

ONfcST' (95 STV»^TS2PSl)0NtST' (96 RT«T22B)) ONfcST' (97 Sl2T»AP*T22T0NfcST' (98

121

^SA-STV.VAT-DR.RT.EAOl.RMVT.BSB-V^^ T.USb*bl2«UBT.DR»RT.STUVn-nJ«D««<VT«ERHS«VV^T«SllT.S22T).DH««' Q^g^pi

W(1J-2,KK) • W(IJ,KK)*AK.<WT<KK)»HAK«WTT<KK)) 570 CONTINUE

QC TQ 600 560 RT » -HR«USA-UU*RSA-2,«B*RR«VSB

UT « .UU»USA*DR*<T11A*2,*B«S12B» VT ■ n, E*U ■ UR«tTll*USA*2.«B«T22*VSR> ET ■ -IJU«ESA*EAD PT ■ RT*PH*ET*PE SUT » -uU«SllA*FRTnMU»(USA-B«V8B> S1<!T ■ 0, S2iT i -00«S22A-TWTnMU«(USA-n«y9B)

ONtST509 0NtST5lu 0NkST9H 0NtST5l2 0NfcST513 0\lfcST514 0vtST51b 0NtST5l6 0NfcST5l7 ONbSTSlP 0NfcST519 ONfcST520 0NtST521 HA. - .RK*ÜAA.;..PSA.OSA:UU.nAA-2.*B«(RSA.VSB*RR^A6> nD.BC1 ., ,^|^^

uii - -üSA.USA.UJ.UAA*DPMTUAA.DR.R5A.TllA*2..B.«St2AB.DR*RSA.S120NtST5^

'IW ..USA.ESA.Uü.EAA*DR.(T11A.USA*T11.UAA.RSA.EA0*,..B.T?2A.VSP-T0NtfcST52.

122»VAB) _ . ,_^_ce» 0NI:ST926 lp*l « HAT«PR*RT«PRS4*EAT.PE»ET«PESA SUAT • -USA.SUA.UU.SUAA^PTJIMUMUAA-B.VAB) 0k)fcST527

0NfcST52H

"dV*, . .UU.S^AB^uPHS.VAB.AyE.MUHMS.USA.B.JVSB^lJB.MnHHS^BB, ONEST^l RTI . •RH'^T-RT.USA.UT.RSA.UU.RAT-^.B.JR^ UTI • -UT«USA-UU*UAT*DR«(S11AT-PAT*2,«B*S12BT-D«*'"TMT1IA«Z. o ±e0NtsT534

UT*ESA«'yU»EAT»DR*((SllT-PT)«USA*Tll«UAT-RT«EAD*2T«R*(S22T-P0NfeST536 0NfcST537 QNtST538 0NtST539 0NfcST54G ONbSTS^X ÜNEST54i 0Nfc5T543 0NtST544 0NfeST545 0NtST546 0NfcST547 0NfcST54P

IB)) VTI ET I

^riTT^^STllluA.UU.SllAUrRTnMU.diAT.B.VPT)

S2^TT ' 2uT*S22A-UU*S22AT-mnmJ«(ÜAT-B*VBT)

DO 590 KK • I.KHAX u„.uu\% H<1J-2,KK) • W(IJ,KK)*AK.(HT(KX)»HAK»HTT<KK))

590 CONTINUE 600 O » VIS«AK.S0RT(<UV»«AX)*«2«<B«VSB*AY)«*2)

!n>02,Kl!)'.1inAj!2.KK)*0.(WSAA(KK)^X..2*HSBQ(KK,.Ar-*)

IF (YIELD.LT.YC) GO TO 650 0NfcST561 ^ |A:l?i-?§,I!p*wS,6.)*USA*(WH<6).AP.HU.7,..VSA^(HW(6).USB*WW(70Nfct^

OMfcSTSS« MDU l)«VSU)-(*<W(5)*WW(7))*WW(3)*nj GO TO 630

122

r

(

620 MCUT B MW(5)*(USA-a*VS6) OhlkSTSbb 630 WDUT»*MAXl(HDOTiO,0) ONkST^S»*

ACUN ■ .9*HD0T«MU*AK/VC ONtST5t»7 SSU ■ {H(IJ-2,5)»*CnN«W(lJ,9>»**2«(W(IJ-2,7>-ACON«H<IJ,y))««2*(W<IONtST5&B lJ-^i6)-*C0N*W(IJi6>»**2«(W(IJ-2,5)-AC0N*W(IJ»9)>*«W(lJii8.7)-*C0N*W0NtST55V 2(|J,7)> OMbST56U AL^HA ■ SQRT(YC/SSO) °N"I"i DC 640 KK ■ 5.7 0NbST562 MtiJ-ZtKK) ■ ALPH*«(W(IJ.2,KK)-AC0N*W<IJ,KK>) 0NbST563

640 CONTINUE 0NEST56« 650 RB ■ H<IJ-2,X) SMU1T = ^

UU • wnj-2,2) 0NtST566 W • H(IJ-2,3) ONbST567

PDtR « .THUE. 0MbST569 PP « PHSJHR.EE) OMbST57U C2 ■ PH*PP«PE/PR»*2 ONfcST571 IF (C2,LT.O.) GO TO 670 ZlllVil C = SOHT<C2) 0NbST573 UC » ABS<UU-ASY(JS*J)*VV)*EIGP(JS*J)«C ONbST!>74 VC » <ABS(VV)*C>*eSV(JS*J> 2

NLSIC,

SB ■ AMAXKUC.VC) 0NbST576 IF (SB.Lfc.SBM) GO TO 660 S^cl«« SBM ■ SB 0^bST578 ISH . |H2 '■JK'bST579 jSd - J ONbSTSBO

660 CONTINUE 0NtSI"i BS • AK.SB ONbSTSB? IF (BS,LT,.9) RETURN 2N!-IE^ WRITE (6,700) IM2.J.AKT,IP0INT,BS,RR,UU,VV,DELX.DELV,ESy(jS*J),MAT0NbST564 GC TO 680 0NbST585

670 WRITE (6|710) IM2,J.RR,UU.VV,AKT.MAT 0MbST586 680 LdJ) - 2 ZtVAll DO 690 KK ■ l.KMAX ONbSTSBK

H(IJ-2IKK) ■ WdJ.KK) S^flrSn 690 CONTINUE OMbST590

RETURN 0MbST591 c 0\'bST592

700 FOHMAT (ilH AT POINT <I3.1H,12,17«) IN OfiESTP AT f.F9.5^8H IP0INT»0NbST593 lI2.3X5HSTAB«F7,4,3X4HRH0.F7.4,3X2HU"r7,4,3X2HV-F7;4.3)'5HDEU*»F5.3.0NbST594

23X!>H0El.B«rs,3.3X8HB SUB R.F7t4,3X4HHAT»I2> e,SN^Ico! 710 FORMAT (ilH AT POINT <I2,1H, 12,33H) IMAQINARY SOUND SPEED IM PNEST0NbST596

lP3X4hRHO»F9.5.3X2HU»F9,S,3X2HV«r9,5,3X2HT«r9,5,3X4HMAT»I2) 0NbST597 EMj 0«lbST598

123

JV». "*i.:s'±::- aajg cja«

SUB^UUTINE BONDRV COMMON// W(2200.75,L<2200) COHMON/BNDCnS/ HB1(109,8,7>,PBI(10«,8>,tNO(109.«), lHHJ(7a,a,7).PBJ(7a,8)iJND(7«|9) COMMON /BNDVAL/ WB(600l7)lrRX(*00)irRV(«00).n(S(600) COMMON /MATARR/ NMAT.lHAT(l2«9)irN«T(23,9).HAT COMMON/SCRTCH/ THB(300t7)«TrR)((300)«TrRy(300)

BONDRY 1NTVAL BNDCRS 8NDCRS BNDVAL MATARR SCRTCH

COMMON /ZONES/ NBEG(9>3).NEND(9<3)«ARC8IZ(9.3)«OlSMAX(9l3).ni9HIN(ZONES 19.3) ZONES COMMON /COMVAL/ KT,AKT.OT.DTMIN,ITER#NEIBR.IROlNT.ERR.E^S.EPSl,RDICOMVAL IS.TOP.DAL.KMAX.RORC.PSCL.LB.LF COMVAL COMMON /MATVAU AX,AYiCrL.VII,VI8T,MÜ,YC.RM0,X0.P0,T0.XZ,A,B,ABUiDMATVAL lABL.CHAN.BMAX.rACT^NR.AF.SBMiAL.AI.AK.HAL.HAS.HAK.OALiO'j.OAK.OAXMATVAL 3 2,nAY.HDAX,HDAY,DAX2,DAY2,HDAXY#00AXV#DTR,HALrMJ

,,TWT0MU.rRTDHU,00VMMATVAL 4 3ü,TREOTM,NI,NJ,NrMAXiIS,JS,IjS,lBS#l8B,J8B,NIMl,NJMl,N0,Nni,NE,NElMATVAL '

4,NF»NIP2,NTR ItVLt^ COMMON /TRCPRT/ NTR8(9),ITR(9,29),TR8(5#25) T?CPRT COMHON /PRESS/ PPER.PP.PE.MATNO ^"EfS COMMON /iNTrC/ NINFC.INrC(60)lNONI^(^0,5) I^TfC |OUlVALENCE<Y2,T0) 0r*x

LOGICAL ERR |TA(Y> ■ BMAX-ALOO((H»A»Y)/<B-A*Y))«ABL ALP(X.Y) . rACT*<X«ANQ«Y«TOPtATAN<Ar«Y)J DO 90 MAT ■ l.NMAT CALL GENVAL Nl ■ IÖS*2 N2 ■ IBS»Nr FRX(IBS*1) ■ ALP(FRX(IBS*1).FRY(IBS«1))*XZ FRY(IBS*l>«ETA(FRY(IBS«l)>*YZ On 10 I ■ N1,N2 FRX<I) ■ ALP(FRX{I),FRY(m*XZ FRY<1)«ETA<FRY<I))»YZ

5

2 ? 2

24 BCNDRV14 B0NDRY19 B0NDRY16 BONDRYl? B0NnRY19 80NDRY20 B0NnRY21 dONDHY22 OFAX 2S 80NDRY24 B0NDRY29 OPAX 26

10 FRSd) • FRS(l-l»*SORT(<FRX(I)"FRX{I«l))*«2»<FRY<I)-FPY(I.l))**2) BONDHY27 DO 60 | ■ l.Nf II ■ rRX(IBS«l)*DAX*1.0 JJ ■ rRY(lBS*I)«U»Y*2,0 DS ■ l.OElO KJ ■ 0 DO 20 J ■ 1.4 K ■ II*M0D(J,2) M ■ JJ*J/3 |r(K,LT.1.0R,K,0T,M,0R,M.LT,2|0R,P,GT,NJ) GO To 20 m ■ IJS*(M-1)*NIP2*K |F (L<MN).EO,0> GO TO 20 .. . , BD • (FRX(IBS*p-FL0AT<K-l)«AX)««2*(FRY<lBS*I)TL0AT(M-l)«AY>»«2 IF (OD.OE.DS) GO TC 20 KJ ■ J DS > DD

20 CONTINUE IF<KJ,fcQ,0) GO TO 60

40 K ■ n*M0D<KJ,2> M ■ JJ*KJ/3 MN ■ IJS*(M.1)*NIP2*« DO 90 KK « i.KHAX

90 WB(IBS*I.KK) ■ W(MN,KK) 60 CONTINUE

124

BONDRV28 S0NDRY29 80NDRY30 80NPRY31 B9NDRY32 90NDRY33 aONDRY34 BCINDRY39 SONDRCll B0NDRY36 80NDRY37 90NDRV3B UPNnRY39 BONDHY40 B0NDRY41 dONDRY42 NSMTHB 1 B0NDRY47 B0NDRY4e B0NDRY49 ÖONDRY90 NSMTHB 2 BONDRY92

90 CONTINUE KETUHN 6ND

8PNDRY65 eONDRm 90NDRV67

125

"tt.'*> •X

CcffiT'bNDVAL/B-fl(*00,7).FRX(600).rpy(600),fRS(600) BNÜVAL Z

COMMON /M4TARR/ NMAT, 1MAT<12,9)iTHif(23,5)#MAT MATAPR 2 CCMMQf' /MATVAU/ »X.AV.Cru.yiS.VIST.MU.YCjRHOjXO.PO.TO.XIjA.B.ABL.DMATVAL 2

lABL.CHAN.BMAX,FACT,*NO,AF,8»H.AL#Ai»AKi«AL,HAS,HAK, OAL.aAS.OAK.DAXMATVAL i 2,C*v<HDAX,HDAY,DAx2.DAY2.HDAXV,0DAXY#OTR,HALFriU,TWTDMU,RRTCMü,00VMMA7VAL < SU.IRtOTM.NI.NJ.NFMAX^S.JS.IJfi.lBS.HB.jSB^IMl.NJMl.NO.NOl^E.NElMATVAL 5 4 IU NIP2 MR MATVAU o

CCMMON /ZONES/ NBEO{5,3).NENr(5,3),ARCai2(5,3),DISMAX(9;3).DIGMIMZnNES 2

^OMMON /COMVAL/ KT,»KT,DT.DTMIN,ITER,NEIBR,lP01NT;ERR.E^S.EPSl.RDICnhVAU 2 IS.IOP.DAU.KMAX.PORQ'.PSCL.LB.LF lli.lt t

CCMHON /PRESS/ PDER.PR,PE.M*TMO "^= f. COMMON /|NTFC/ NINFC,INFC(60>,NONIN(20,5) J^;^c i ECUIVALENCECYZ.TO) "[**, " LCülCAL PDER g||g "

D«i* HAXIT/IO/ S:.:pc;; H(Y)iA-B»(CHAN«*t9MAX-Y*YZI-1.0)/«CMAN««(BMAX-Y*YZ)«1.0> OFAX 33 Z(X,Y) « X0«(X-XZ)»ANO«y«TCP«ATANUr«Y) DtNSB *'

NIN2-2.NINFC*! Hill [l DC 10 MAT - l.NMAT JENSB 1« DC 10 I ■ 1,NIN2 2|"|5 iß

10 NCMNd.MAT» - 0 "NSB 20 DC 70 K ■ I.NINFC S|^5 || MAll . INFC{6*K-5) PENSB Z; MAI2 . INrC(6«K.2) JlJJfg ^4

Nl « lNFC«6*K-4) °^^ ^

IF <NONIN<IJ,HAT).NE,0) QO TC 30 DENSP Z* 40 IF UJ.EQ.l) SO TO 90 .. °|£|* 3?

IF <N0NIN(IJ-1,MAT),LT,N1) 00 TO 50 D|NSB 31 NONJNdJ.MAT) ■ NONIN(IJ-2,HAT) ^ENSB ^ N0NIN<|J*1,MAT) » NONlNUJ-l.MAT) g|JJ|B 33

Jo ToTo2 DENSB 35 50 NONlNdJ.MAT) - Nl °|^B 36

N0NIN(IJ»1,MAT) . N2 lllll H ,Fi(MAT.EQ.MAT2) GO TO 60 J|^ '«

Nl « INFC(6.K) JIKIg JJ 11 ■TOT0

c,6#K'l, 60 IBS . IMAT<7,MAT2) D^|B *J

Nl - IHS.INFC«6«K) J^SB 44 N2 » 1BS*INFC(6*K-1> S|K|5 ^ DC 70 J ■ N1,N2 JE^P "

70 HB(J,1J ■ -WB(J,l) SINIB 48 DO 220 MAT . l.NMAT Jf^J ^ CALL GENVAL ll^ll H DO 80 J ■ l.NF DENSB 50

126

I » IHS*J DEN^B bl TfHYCJ) • R(rBr{I)) DEN3B ^^

ao TFKX(J> ■ z(rRx<l).TFHr(j)) DENSB »J U ■ 1 DENSB 54 Nl • 1 DENSB Sb N2 ■ NONIN(l,MAT) DENSB bt If (N2,Nfc,0) GO TO 100 DENSB *>7 Nl « IdS«l DENSB 5« N? • IbS^NF DENSP bV 00 TO 11(3 DPNSB 60

90 U ■ IJ*2 DENSB 61 NJ ■ NONlNdj.j.MAT)*! DENSB 62 N2 » NONJNdJ.MAT) DENSB 65 IF (N2,NtiO> GO TO 100 DENSB 64 IF (NliGT.NF) CO TO 1V0 DENSB bb Nl » IdS^Nl DENSB 6e N2 » IHS*NF DENSH 67 GC TO HO DENSH 6«

100 IF <N1,E0(N2) GO TO 90 DENSB 69 Nl » IHS-Ni DENSB 70 N2 « iaS«N2-i DENSB 71

110 DO 100 I ■ N1,N2 DENSfi 7? j z i.IBS dtHSB ti IF (J.NE.l.AND.J.NE.NF) GO TO 140 DENSB 74 IF (TFWY(J>,GT.l,0E-4) GO TO 120 DENSB 75 CCbPSl ■ 0.0 DENSB 76 SINPSI « 1.0 DENSB 77 GC TO 16U DENSB 7«

120 IF (J.hQ.NF) GO TO 130 DENSB 79 jp • ? DENSB eo jH=NF-l DENSBC21 60 TO 15Ü DENSB 02

X30 JP»2 DENSBC22 jf- a NF-j DENSB 84 GO TO 150 DENSB «5

140 JP ■ J*l DENSB 86 j»« ■ j-i DENSB 87

150 DZ ■ TFRX(JP)-TFRX(JM> DENSB 86 DR ■ TFRYCJP)-TFRV<JH) DENSB 89 COSPSI » DZ/S0RT<DZ»*2*0R««2) DENSB 90 SINPSI » DR/S0RT<DZ**2»nR««2) DENSB 91

160 CONTINUE DENSBC12 PP ■ Hb(I»5)«SINPSI«*2«2.0*U',(I,6)«SINPSl«COSPSI*WB(Ii7l»CCSPSI**2DFNSB107 E » WB(!,4) DENSBIOS PDtR ■ .TRUE. DFNSB109 DO 170 H • 1,MAXIT DENSB110 RHU • -Höd.l) DENSB111 P » PRStRHO.E) DENSB112 COH» • (P-PP)/PR DENSBH3 WBlI.l) > WBd.D-CORR 5EI)JSoiK IF(*HS(C0«R),LE.ABS(WB(I,1)>«EPS1) QC TO 180 DENSBC13

170 CCNTlNyE DENSB116 ERH ■ .TRUE. DENSB117 MfilTfc {6,230) AKT,M4T,J,E,PP,WB(Iil),P#PR.CORR UENSBllB

160 CONTINUE DFNSB119 IF (NONIN«IJ,MAT>,NE,0> GO TO 90 DENSB120

127

ff 0m

DENSB121 190 DC 22(1 M ■ 1,3 DENSB122

Df'AX « 0,0 DENSB123 CIN i 1,0E6 DENSB124 Nl ■ IBS«NBEG<MAT,M>«1 DENSB125 N2 ■ IHS*NEND(HAT,M) DENSB126 WB«N1«1.1)"*BS(HB(N1-Iil)) DENSH127 OC 210 I ■ Nl,N2 DPNSB12B IF (HBUiD.GE.O.O) GO TO 200 DENSB129 WB(I|1) ■ -WBd.l) DPNSH130 GC TO 210 DENSB131

200 DUDIS « FRSm-PRSn-D DENSH132 OMAX ■ AM*X1(DMAX,DIFDIS) DENSB13J DPlN ■ AMlNKDMlN.DlFDl») DENSFU34

210 CONTINUE DENSB135 DIijMAX(M*T,M) ■ DMAX DENSB136

220 DliMINCMAT.M) ■ DMIN DENSB137 REIURN DENSB13Ö

1 230 rCKMAT (6H0AT T.r9.,.38H DENSITY DOES NOT ^ERGi CN HATF«ULI2. J^BCJJ 118H BOUNDARY AT POINT M/19H0F..P^''HOl P, PR.CORS/6E20 .7) DENSB141

ENÜ

128

i^.ijfcij'

SLdROUTINE INFACE INFACE ? COMMON /BNDVAL/ •<fl(AOO,7),rR)((600),rPY(6CO),rRS<600) BNÜVAL 2 COMMON/SCHTCH/ TWR(3OO,7),TrRX(30O),TrRY(30O> SCHTCH 2 COMMON /MATARR/ NMATc I MAT(12#9).FMATCaS.S)iMAT MATARR 2 COMMON /ZONES/ NBeGr5.3),NEND(5,3),APCSIZ(5.3),DISMAX(5'.3>.DISMIN(Z0NES 2

15«J) ZONES 3 COMMON /COMVAL/ KT.AKT.DT.DTMIN.ITER^EIBR.lPOJNT'.ERR.ERS.EPSl.RDICOMVAL 2

ISI IOP,üAt.,KMAX,PORQ,,PSCL.LB.Lr COMVAL -5 COMMON /PHESS/ PDER.PR.PE.MATNO PRfcSS 2 COMMON /JNTFC/ NlNrc.!NrC«60).NONlN(?0,9) 1NTFC 2 LCblCAL PDER.ERR INFACI 1 D*IA MAXIT/10/ INFAC1 ? 2(X,V) . FMAT(9iMAT)«(X-FMAT(12,MAT))*rMAT(20.MAT»«y«TOP«»TAN(FMAT|NFACEll 1(21,MAT)«Y) INFACE12 Ch(r).FMAT(17.MAT)**(rMAT(l8,MAT)-Y*FMAT(H,MAT>) OFAX 3^ R(Y) a FMAT(l3,MAT)-FMAT(14,t'AT)*<CH(Y>.l.O>/(CH(Y)*1.0l INMCE14 PCfcRa.TRUfe. iNfACl 3

IM ACE16 IMFACE17 INFACElP INfACE19 INFACEZO INFACE21 INFACE22 INFACE23 IMFACE24 INFACE25 IMFACE26 INFACE27 IMFACE2e I^FACE2,' INFACE3C INFACE31 INFACE32 INFACE33 INFACE34 INFACE35 INF ACF36 INFACE37 INF.C2 1 INFACE39 INF AC? 2 INFACE41 INFACE42 INFACE43 INfACE44 lNFACE4t> INFACE46 INFACE47 INFACE4? INFACE49 INFACE50 INFACE51 INFACE52 INFACE53 INfACE54

129

UO 6Q K ■ l.NlNFC HAU « INfC(6*K-5) MAI2 ■ INFC(6«K-2) Rf-Ul « FMATOiMATl) RhU2 » FM*T(8.M*T2) RH12 ■ RM01*RH02 IBs ■ IHAT(7,MAT1)

Nl > IbS*lNrc(6*K«4) N2 * IUS*lNrC(6*K-3) NF ■ NbNü<MATl-3) MAt ■ hATl J * iMAU7,MAT2)*INrC(6«Kl -1)*1 DO 60 I ■ N1,N2 J » J-l IJ ■ i-ias IF (IJ.Nfc.l.AND.IJ.NE.NF) GO TO 30 IF (FRY(l).GT,1.0E-4) QO TO 10 COSPSI « 0.0 SINP5I ■ 1.0 GO TO 50

to IF (IJ.EQ.NF) 30 TO 20 IP i IUS*2

GO TO 40 20 IP*IgS*2

if ■ iös»Nr-i GO TO 40

30 IP ■ !♦! If ■ I-l

40 RP ■ R{FHY(IP)) Rf ■ R(FRY(1M)) OR « RP-RM DZ ■ Z(FRXJIP),RP)-2(FRX<tM),RM) CObPSI » DZ/S0RT(nZ»*2«DR ••2) SlNPSI » DR/S0RT(n2««2*DR ̂ •2)

50 M*TNO ■ IMATdO.MATl) RMU ■ HB(Iil) E » WB(I(4) PI ■ PHS(«HO,E)

MAINO • IMATdDtMAT?) H^U ■ WBU.l) E > MBU.4) P2 • PHS<RHO,E) SINSQ ■ SINPSI**2 CObSQ ■ C0SPSI**2 SINCOS ■ SINPSI*C0SPSI TKNl ■ (WB<I,5)-Pl)*SINSO*2.0«HI<li«)*SINCOS»(HB(|,7)«Pl)«COSSO TKN2 • (wa(J.5)«P?)*SlNSü*2,C«H«(Ji«)*SlNC0S»<WBU,7)«P2)*C0SS0 UM ■ MB(lt2)*SINPSl*WB(I.3)«C0SPSI UM ■ MB(Ji2)*SINPSI*WR(J.3)«C0SPSI UTl t WB(1,3)«SINPS1-WB(I.2)*C08P8I \JM ■ V«B(J,3)*SINPSI<WB(J.2)«C0SPSI TKN ■ RHl2«(WP(Jil)«TNNl*WB<lil)*TNN2)/(RH01*wB< r.l)*PH02«WB(Ji1)) TNN1 « TNN/RH01 TK.M2 « TNN/RH02 CCINI » RH0l«WR( Iil) CCM2 « RH02*WP(Jil) UN ■ (C0Nl«UNl*C0N2«UN2)/(CO'!l*C0N2» »6(1,2) ■ UN»SINPSI-UTl*COSPSI WBU.2) ■ UN*SINPSl«UT2*COSPSI UB(||3) ■ UN*COSPSI*UU*S!NPSI W'jlj,3) ■ UN*C0SPSI*UT2«S1NPSI TNN'TNNl M*I"M*T1 M»l

52 M*1N0»IMAT<10,M*T) IF(MATNO,QT,103) GO TO 96 EIMB(H«4) PPsHÜ(M,5)*SINS0»2,n«HB(M,6)«SINC0S*WB(H,7)«C0SSQ»TK,N DC 54 N«1»MAXIT RhU«-WB(M»l) p*HRS(HHOtE) COHRi(P-PP)/PR HBCM.DiWaCM.D-CORP ir(AHS(C0PR),LEiARS(W6(H,i))*FPSl) OC TO 96

54 CONTINUE tRHi.THUfc, MMsM»lM*T(7,MAT> HRjTfc(6.l00) AKT,MAT,MM,E.PP,HB(M»l),P,PRiCOPR

56 IF«MAT,EQ.MAT2) Sd TO 60 TNN"TNN2 MAI»MAT2 M»J GO TO b2

60 CONTINUE RE1URN

100 FOHMAT (6M0AT T«r9,5.3SM DENStTY DOES NOT CONVERGE ON MATESIALI2I 118H BOUNDARY AT POINT 14/19H0E.PP»«HO,P,PRiC0RR/6E80.7»

ENU

iNFACESb INFACE56 IMFACE57 iNFACEje lMhACE59 iNfACE6G INFACE61 |NF/kCE62 INFACE63 INFACE66 INFACE67 INfACEöP INKACE69 IMfACE7Ü INFACE71 INFACE7? INf ACE7!> INFACE76 INFACE77 INUCEB4 INFACEöS INFACEBo INFACE87 INFAC1 4 INfAC1 INFAC1 INfAC1 |Mf AC1 INFAC1 INFACUO INfAClll INfACli2 INfAC113 INFACli4 INfACliS INf AC116 INFAC117 INFAC118 INFAC3 1 INfAC3 2 INFAC121 IMFAC122 INfAC123 INFAC124 INfAC125 iMFACESa INfACEe9 INFAC126 INFAC127 INFACE90

150

t&tift

SLriRüUTINb FINISH ^T1!^ , CCMMüN// WI?200,7),L(?210) ,n n4 IZiiUk i CCMMUN/RNDCRS/ WBI(lO,>.a,7),PRI(l09,P)iIK,D(109,9), BNUCH5 2

lWbJ</8,e,7),pHj(78,M.jMn(7«,9> Lmwii5 i COMMON /BNDVAL/ *Ruoo,7).rRX(600),rpY(600),rRS(6P(n , .^„.„JSr^c 9 COMMON /ZONES/ NBFG(5,3).tlENr(5.3).ARCSIZ(5i3».niSM*X(5.3).niSMIN(Z0NFS 2

15,0) Z0NtS .3 CCMMUN /MATARR/ NMAT, IM*T(12,5),FMAT(P3,5)»MAT MATARR i?

ggÄ ^KI; rT:^5T!fi:s^i2N!i^^ii^:.pn,NT.EPP.EPS.Eps..RD.5o^LT.

lAfiU.CHAN, dMAX,FACT, ANn.AF.SRM.AL.*S.AK, MAL.HAS.HAK,rAL,IAS,OAK, PAXMATVAL S ?,CAV,HOAX,HDAV.DAX2.DAY?.HDAXV,0DAXY,üTR,HALrHU,TWTrHII,FRTrMl,0OVMMATVAL < 3U,IHfc0TM,NI,NJ,NrMAX.lS.JS.IJS,I0S,IfR.JSn.NPl.NJM1,^D'.Nin.Kl:,NElMArvAL b

4 ^^ NIR? "TR MATVAL " COMMON /INTFC/ NIMFC. INFC(60).NONIN(20,5) i^'J^cu,^ LOülC*L fcHR F 1HI3 ZbMAX I AX.FL0AKNIM1) r cu,!« RhMAX • AY«FLnAT(NJ.2) c K cuK

I«: '-ill' n?!!^ WX ■ ZMX Rf'NiZMN

DO 10 I ■ l.NF r,N.,cu,Q Z^M ■ AM1N1(ZMN,FKX(IBS*I)) r N CW90 ZMX ■ AMAXl(ZMX,rRX(IBS*I)) nrAv TA RMNtAMlNltRMN,FRY(IRS*I)) r,ficu91

10 RMX I AMAX1(RMX,FRY(IBS*I)) „i.v li IFCRMX.Gfc.RPMAX.OR.PMN.LT.-l.OE-O (?C TO 60 r.^cu^

IFCZMN.Lt.O.O) GO TO 15 r N SH7« IF(ZMX,LT.ZRMAX) GO TO 70 r ^ cu« ISH»1NT(ZMN»DAX) K<U

ÜC TO 18 15 ISM«INT( (ZMX-7BMAX)«DAX)

t<«Nl*i ISC»-1

20

00 30 KK ' l.KMAX 3D

FINISM17 OFAX 3b fIMISHl?

FINISH26 .._. FIMSH27 ,r T^ 1« FINISH2H

FINISH29 FINISH30 FINISH31 FINISC21

16 ISH.lSM/i jSM»lAbS(ISH) F1NISC2Ü IFUSH.LE^) GO TO 60 FINlSN3i ZD^ ■ FLOAT(ISH)«AX FIMSH34 XZsXZ-ZDF FINISC23 FfAT(l2,MAT) ■ XZ FINISH36

FIMSH37

FRX(I0S*I)«FRX(I9S»I)-ZDF c ^ CUAO

ISH.JSH.l F N |S3S

IMI sS FINISH42

f IMISH46

W(JJ*K,KK) ■ W(JJ*I,KK) FlNi&M'

131

40

50

60

70

DC 40 j « 1,9 1NU(IS*K,J) a piD(IS«IiJ) DC 50 {»liJSH K"H*1NC DO 50 J ■ 1,NJ JJ ■ IJS«(J-l)«NiP2 L( Jj«K)iO HRlTb (6,170) UAT.ISH GO TQ 70 fcRN ■ .TRUE,

WRiTfc uIzoO) ZBMAX,RPH*X.(rPX<lBS*n#FPy(IBS*I>,I ■ 1»NF» DC 150 H « 1,3

eo

90

100 110

120

» NfcMO(M*T.M ■ NUEQlMATiM)

130

LE DELS » FHS(lBS*LF)-rRS(irs*Lr> IF (Z.O'AHCSIZjMAT.Mj.GT.PF.Lr» 00 TO 130 LAuD « (LF-LB)/2 IF <NF»LAÜD,GT,NFMAX) Gn TO 130 Lf • NF-tf IF (LM.EU.O) OCJ TO 110 DO 60 1 ■ 1,NTR IF tlTH(MAT,n,LT,LF) GO TO 60 ITH<MAT,1) • ITRCMAT,I)*LAPn CONTINUE NIN2 « 2«NINFC DC 90 I « 1IMN2 IF (INFC(3«I-2),NE,MAT) GO TO 90 IF (INFCJJ«1.1),GE.I F) INrC(3«l.l) ■ INFC(3*1-1>*LA0D IF «INFC(3*1),GE,LF) INFC(3«I) • INFC (3* I^LAOD

CCNTINOE NF1 ■ NF*1 DC 100 UC ■ 1»LM LI • NF1-LL L2 » L1*U*DD FRX(IBb*i.2) « FRX(IPS*L1) FRY(IBS*12) ■ FRV(IRS*L1) DC 100 KK ■ l.KMAX wBllÖS*L2iKK) ■ ^R(IBS*Ll.KK) CONTINUE DO ViO LI ■ M,3 IF (LliEQ.l) GC TO 120 NBtG(MAT,Ll) ■ NEND<«ATiLl-l) NENDJMAT.LI) ■ NEND(MAT,L1)«.LADD NF ■ NF*L*D0 NE ■ NENU(MAT(2> NEl ■ NE*1 NC • NbND(MATil) NDl • ND*1 WRITE (6,190) KAT.M,DELS,ARCSIZtHAT.p),AKT ARCSIZ(MAT,M) E DELS GO TQ 14Ü DELS « DELS/FLOAT(LF-LB) IF (DISMlN(MAT,M)lGE,(1.0-DAL)*OELS.AND.riSMAX(MAT,H)iLB.(1.0*DAl.)

l«DtLS) GO TO 150 WRITE (6,160) MAT.M.DELS,DISHIN(MAT,M,D!SMAX(MAT,M>,AKT

FINISH48 FINISH49 FIN1SH60 FINISH51 FIN1SH52 FINISH53 FINISH54 FINISH55 FIN1SH56 F1NISH67 FIMSH58 FINISHS? FIMSH60 FINISH61 FINISH62 F1MSH63 FINISH64 FINISH65 FINISH66 FINISH67 FINISH6Ö f JNISH69 FINISH70 FINISH71 FINISH72 FIN1SH73 FIN1SH74 FINISH75 FINISH76 FINISH?? FINISH7e FINISH79 FINISHBO FINISHBl FINISH82 FINISHB3 FINISH84 FINISHB5 FINlSHe6 FINISH87 FIMSHB8 FIN1SH89 FINISH90 F1MSH91 F1NISH92 FINISH93 FIMSH94 FIMSH95 FINISH96 FINISH97 FINISH9e F1MSH99 FINIS100 FIMSlfll FINIS102 FINIS1Ö3

132

^wmmmnmmußf*

140 CALL RfcLAÖL (M) 150 CONTINUE

REIUHN

160 FCWMAT (löH RFZONINR MATFMUL!2.8H SLRFACF 12, 6x5H^ELr,.ri 0 .7, 6X7HD

iSf 1N«F10,7,6X7HDISM*X»F10.7,6X2HT«F915) .,,.,. 170 FC^MAT (9H0MATERULl2.3nH POI.'NDAHV EXCEEHr: DCAIN SklFTtS) 180 FCHMAT (9H0MATERlALt2.3(SH ROPMDARV EXCEEPS M'U j^RUtj *«0^") 190 FCHMAT (26H AUPINr, POINTS Tn MATERIAL 12.5H SI DE 12. öxa^AICS I 7E.F1 2

1&.ÖX12HOLU ARCSlZFiri2,5,6X2,IT»F9,5) , . . ,. ,. ,,.. 200 FCHMAT (24H0(ZHAX.RMAX)/(Z(I).R(n)/F11.3,F9.3/'(6!Fn.3.F9.^)))

fcKJ

F INI 51 0-1 FINIS10K

Fimsino FINIS1C7

IFINIS1Ü*- FIMSIO'J FINISH J FINISH!

.FINISH^ FINIbllJ FIMSn« FINISU'J

133

iäüM

SLbRüUTIixt RELAHt (M) CCMMON /H^DV*L/ WH(AOni7)1FRX(600>»rrY(600)irr'S(6no) CCMMON /ZONFS/ N3FG(5i3),fJfNri(5i3)iAFCSIZ(5i3).ni5!M4X<5',3

I61.J) CC1M0N /HATAHR/ NMAT.IMAT(1?,5),FMAT(23,F)»MA^ CCMMON/SCRTCH/ T/m(300,7),Trrx(300>#TFRVnOO> CCMMQN /COMVAL/ <T,»KTlDT,DTHlNinER,NEIFP.IPOlrjT,EflR,EPS

IS,IOP.UAUIKMAX.PDRG.PSCL.LB.LF CCMMON /MATVAL/ AX.AYiCPL,VIS.VIST,MU.YCjRHO.XO.PO.TO.XZ,

lAPL,CHAN,HMAX,rACT,»Mr,/4F.SnV,AL»*S,*K,HAL.HA^,HAK,CAL.0A ?,CAY,HDAX,HnAY,PAX2.DAY?,HDAXY,ODAXV,DTPiMAt.rMu,Ti-TrMr,rp 3U. IHbOTM.M.NJ.NFMAX, tS.JS.IJS, IBS, ISB, JSf.NIMi.fiJMI »K'O'.N 4,Kf .MP?,NTR

CCMMQN /THCPRT/ STR«!<5), ITR(r,25),T»S(5.2,?> CCMMON /INTFC/ NlnFr,INrr(«0),HONINf?0,5) ÜAIA EPS/1.E-5/

10 MF NF

c LB c NB c Lt c MF c

» NtMÜ<MAT,r) » NdEu(MAT,H) IS THE ÜEGINMINC UF THF OLH IS THfe BEGINNING OP THE NEW IS tHfe END OF THF OLP SET IS THE END OF THP NEW SET

SET SET

NBi ■ N8*l NFM1 s MF-1 DELS « (FNS(IPS*LF).FRSnF;S*LB))/P|.OAT(MF-NB) S = FRS(töS*LP) K » LB*1 DC 20 J ■ 1,NTR IF (ITH(MAT.J).GE,La) C1 TO An

20 CCNTJNUE 30 STN > l.üEin

IJ ■ l>*i GC TO 00

40 IJ « ITR(MAT,J) IF (IJ.GtiLP) GP TO 30 STH ■ FRSUPSMJ>*TnS(HAT.J)«(FRS<lPS*lj*l)-rns(IRS*lJ) )

50 CCNTINUF DC 110 I ■ NBl,Nf>i S = S»DELS

60 IP <FRS( lHS*K).r,E.S) GO TO 7r K * K*l GC TO 60

70 AO ■ (S-FHS(IHS*<))/(PPS(IRS*K-l)-FRE(IRS*Kn Al ■ 1,0-AO TFHXtM • A0«FRX<I8S*K-1)*A1*FRX(IES*K) TFKV(I) « A0«FRY( IB<!*K-l)*Al«rRY( IBS*K) DO 80 KK « l.KHAX

80 TUd(I.KK) » AO*wa(lBS*K-l,KK)*Al*WB(lPS*K,KK) <»0 IF (STH.üT.S) GO TO 110

ITH(MAT.J) = 1-1 TH!>(MAT.J) ■ (STR-S*neuS)/nELS J = J*l IF (J.GT.NTR) GO TO 100 IJ » ITR(MAT,J! IF (IJ.Gt.LP) (.0 TO 100

RFL BMU

),niSMlN(2nN ZON MAT SCK

.EPSJ.RDICOM CTM

A,P,ABL#DM4T S,0At>#rAXM4T TCMUiOf'VMMAT rl.NF.NElMAT

MAT TPC 1'iT RFL RTL HFL RFL RFL RPL RFL RFL RFL RFL RFL RFL RFL RFL RFL RCL RCL RFL RFL RFL RFL RFL RFL PEL RFL RFL RFL RFL RFL RFL RFL RFL RFL RFL PEL KEL RFL RFL RFL RFL REL

AHL 2 VAL i FS ? FS J

«RR ! TCH ?

VAL ^ VAL 3 VAL 2 VAL i VAL * VAL '/ VAL <■ PhT k rr ? AFL11 AHLli iHLU AHLl-t AHLlb ABH6 AHL17 AhLlf AHL19 AhL20 ABL21

AF;L22 AHL23

AHL2« ABL2b AbL26 APL27 AfiL28 ABL29 AhL3n ABL31 ABL32 ABL3J ABL34 ABL35 ABL36 ARL37 ABL3fi AHL39 AHL40 ABL41 AEL42 AEL43 ABL44 ABL4b ABL46 ABL47

AHL4fi ABL49 ABL50 ABL51

134

^

STrt i FR!»(IBS*IJ>»T0S(H*T,J)«(rRS(lBS*lJ*l)-FnS(19S»IJ)> UC TO VO

100 ST« ■ X.UklO U » LF*1

110 CCNTINUE IF (U^t.LF) GO TO 13Ü UC 120 1 ■ J.NTR ly » rTR(MAT,I) If (UiGE.LF) GO TO ISO STH « rRS(IBS*lJ)*TBS<M»T,I»*<FRS(lF,S*lJ*l>-'nS<lHS*lJ)) ITH(M*T,p ■ NFM1

120 TKaCHAT.I) ■ (STR-SJ/DELS 130 CCMTINUE

TFr(X(Nb) » FRy<IBS*LB) TI:«¥«NH) ■ rRY(lBP*LB5 TF«XtMF) ■ FRXdBS^LF) TF«Y(Mf ) « FRY(ia5*LF> UC 140 KK ■ l.KMAX TWö(NB,KK) ■ Wf.t IHS^LHJXK»

140 T»«tJ(MF,KK) ■ WB( IRS^LF^K)

wt HAvt JUST FcuNn ru ANr FV

DC 150 I ■ NBiMF FfiX(IRb*l( ■ TFRX(I) FfiY<IBS*l) ■ TFRYm DC 1»0 KK ■ l.KHAX

150 WPlIbS«I|KK) • TiiB<JiKK> TFHX(i) a 0.0 DC 160 I » 2,*JF TFHXtn ■ FRSUBSM)

160 FRb(IBb*I) • FpslIB«!*I-l)*SQPT((FRY(lBS»I)-F!?YlIPS»I-l)>«

1BSM)-FRX(1BS*I-1)>*«2) N1N2 « 2«NINFC Nl ■ IbS*NBl N2 ■ IliS*NF DC 220 I • l.NIMZ IF «INFC»3*I-2),VF.M*TJ GO TP 22" U « MüD(I,2) Kl »rj'I-U 11 « INFC(Kl) K2 ■ 3«I-1*IJ 12 » I>(FC«K2) If Ul.Lfc.Ln.OP.U.nT.LF) GO TO 190 S = TFHXUl)

170

180 190

200

DC 170 J « Nl,N2 IF <S.LE.FRS(J)) CCNTtNUE J s N2 IN^(Kl) ■ J-IbS IF (12.Lfc.LB.0p. S - TFHX(I2) DC 2C0 J ■ NliN2 IF tS,LT,FRS(J)) CONTINUE J = N2*l

RÜ TO 160

l?.f!T.Ln GO TO 220

r,0 TO 210

HELABLi)? RFLAbL!».' RELAHl t>i RFLAHLb1? REUAbLh'' RELAhLb/ RELiHLiC RFLAHLb1' flFUArlL^r

REUAI'LM HFLAH h? RELAI-Lb ' RFLAhLb" RFLAHLftK

RFLAhLhf RPLAHLh? Rf-LAhLftf RFLAhLh'« HFLAhL?" HFLAHL71 RFLARL?;1

»ElAbL?^ HFLAHL?«» RFLAliU7'' RFLAbL7^ RFUAHU?' HFLAfiL?" RFUAbU7V HELABLH.T RFLAHL81 RFLABLÖ^

^♦(FRydHFtAHLH.1

RFLAPLÖ« HELAfcLÖ'J HEUAbLHt RFUAbL87 RELAHLKf' RFUAbLS'v HFLAbL9j RFLAbL9l RELABL92 HELAHL93 HFLAHL9« HrLAbL9b RELAbL9f! R[!LAHL97 REUABL9(i, RELAbU9<' RFLAH100 RELAlnOl RFLAbl0:j

RFLAblOJ RFLABIO1» RFLAblU"5 HFLAHlU'i HELARIO;

135

k^.

210 INhC(Ka) 220 CONTINUE

HMUHN EMJ

J'1-I3S RELAhlG^ RELAf'lOV RFLAbllO RELAblll

136

tJjstä

SLbHOUTlNfc BPOSN 4.ft „,. CCMMüN/BNUCRS/ wBl(lO,',8,7),rni«109,8>,lNn(l(l9.9), lHBJ(7eiS,7)#PBj(7fl,«).JND(7B»9) ,% P-«,,^«. CCMMON /HNDVAL/ rfH(1SOO,7).rRX(600),rFY{600).rRS<6CO) CCMMON /MATARR/ NMAT, 1MiT(1?,5),FMAT(23.5)#M*n c.c coe, CCnMON /COMVAL/ KT, *KT, nT.DT!1!N. ITEP,NEIt'R, IPdNT . EBP.EPS, EPSl

ISI IOP,UAL»KMAX,PORG.PSCL.LB,LF _, ^K W(| Bn .-„,.„. CCMMON /MATVAU/ »X.iY.crL.VlS.VIST.Ht.rC.PHO.XO.PU.TO.XZ.A.P.A lA^L.CHAN.HMAX.FACT.ANO.AF.SBlSAL.AS.AK.HAL.HAS.HJK.CAL.IAS.nAK 2%AY%ÜAX,HPAY.DAX2.DAY2.HDAXy,0DAXY,DTP,HALrMU,TWTCMU,rRTrKU. SU.iREOTM.M.NJ.NFMAX.IS.JS.IJS.IBS.ISB.jSB.NIMi.MjMl.K'D.Nnl.NE 4,^^,N1P2,MTR LCüICAL fe«H U*iA IH.JM,fXSI,MxSJ/2HI..2Hj.,8,8/ DC 10 I ■ liNl

io INLM:S*I.I> S o DC 20 Jsl.NJ

20 jNiJ<jS«J,l) x 0 1A s FHX(IBS*l)*DAX JA = FHy(IBS*l)*DAY lFiAbS(rHY(lBS*l>),LE.1.0F-«) JA»-1 DC 170 L " 2,NF It » FRX(IBS*L)»DAX Jb » FHY(IBS*U*DAY IFlABS<rRY(lBS*L)).(,>.T,1.0F-4) GO TO 30 lAslb JF--1

30 IC » Ib-iA IF (ICJ 40#100,50

4n \P « IA*1 1* « IA-1 ÜC TO 60

50 l« » IA*i '.P » IA*.

6U K = INU(li IP.1)*1 IF (K.uT.MXSI) GO Tf) 90 INJ(IS*IP»1) - K

70 IF (K.fcO.l) GO VO 80 LA ■ INOdSMP.K) IF (rRY;iHS*LA).LF.FRY(IPS*L-l)> GO T0 PC IKJtlS*lPiK*H « !Nn(IS*lP.K) K = K-l GC TO 70

80 1MJ(IS*IP»K':) ■ L-1 GC TO JO

90 WRITS (6,180) IH,IP,MAT.MXSl.AKT ERH ■ ,THUE,

loo je ■ ja-jA IF tjcj uo.i'o.m

110 JP « JA*2 JA » JA-i GC TO 130

120 JA » JA*1 JP • JA*2

130 K = JND(JS*JP,1)»1 IF (K.GT.MXSJ) GD Tn 160

ÖPÜSN 2 BRUCHS 2 BN1JCKS 3 BNDVAL ? MATAPR V

.FDICOMVAL COMVAL

Bt.nMATVAU .TAXHATVAL OnVMMATVAL .MElMATVAL

MATVAL 'I BPOSr BPUSN '' BPOSN 1 ! Bpusr. li BPUSf BPur.f. BOU'N BPU^r. 1'J

BPUSf Ifr BPU<;N 17 Bpusr ypusr Bpusr- zn

Bpus^l ?.\ BPÜSN 22 BPUSN 2:( Bpus^ 24 BPUSN ?.b BPUSN Zfc BPOSf 27 BPÜSN 26 BPOSN 2' BPÜSN bPUSI> BPUSN BPUSN 33 BPÜSN 3« BPUSN 35 BPUSN 36 BPOSN 37 BPOSN 36 BPOSN 3' BPOSN «0 BPUSN 41 BPUSN 42 BPUSN 43 ÖPUSN 44 BPUSN 45 BPOSN BPUSN BPUSN BPUSN 4V BPUSN bT BPCSN 61

U 1.»

i- i'-

3 0 31 32

46 47 4H

137

"1

140

150

160

170

180

JNU(JS*JPil) ■ K IF (K.kO.l) GO TO 110 L* » JNDUS*JP,K) IF {FPX(IHS*L*).LF.rRX(IBS*L-l)) QO Tu 150 JNÜ( JS*JP»K*1) ■ JNnUS*JP»K> K « K-t GO TO 14U JNU(JS*JP»K*1) • L-l GC TO 10U WBlTfe (61I8O) JH, JP.MAf.MXSJ.AKT EfiH i .THUE, COiNTJNUE HFlURN

FOKMAT (4H0AT A2,12.9H MiTERI AL. 12.?™ nCliNOA^V COSSED MPPF THAN 12.öH TiMfeS3X2HT«ro,S) ENÜ

BPÜSN BPOSh BPUSr: BPUSN BPOSK BPOSN BPUSN BPOSr. BPUSN BPUSN BPUSN BPUS'. BPUSN BPUSN IBPUSN BPUS^ BPUSN

S2 Si

5b ^6 t>7 50

60 61 62 ti 64

6,3 6') 67 6«

138

CCMMOM /COMVAL/ KT,»KT.nT.MfMN. ITEH.NEIBR, iP0INT,E»R.EI»5.f PS1.» UJva^^^ ^

4,Nf,NIKc|NTR BVALU 7 DC 20 l ■ liNl BVALÜ *■ N = INüdS*!,!) BVALU Q

IF (N.bQ.O GO TO 20 HVAL(; xr X = FL0AT<I-1)«AX BVALL 11

DC 10 K ■ liN BVALU 12 «;<ls!'l|^';'<?ät,,.s.L..(x.r«(1»s.Ln..rRY1lBs-L.11.r.Y.l.s.L>./B«|;riJ

*o . (s-FRS(iRs*L*i»>/<fRS(irs*L)-rRS<i"R*L*l>) llllv li

^US^K.J^^AO^il^L.KK.^.BCirS^l.KK, JÄlJ 10 CONTINUE BVALU 21 20 CONTINUE BVALU 2^

DO 50 J»2.NJ BVALL 23 N = JN0(JS*J»1) BVALU 2* If (N.tO.O) GO TO 50 BVALU 2^ Y a FLÜAT(J-2)«AY BVALU 2t

P^ÄiV?" l..,».r»,III.s.L...<FRxii»W....F.«..BS.L..m;S|e

AO » (S-rRS<lBS*L*l)W(fRS(lPS*L)-FRS(IBS*L*in BvALL 3?

Al ■ 1,0-AO BVALU ,53 SL^.^^r^.O.WRCB^L.KK.^.WBdES^l.KK, BVALt^

40 CCNTJNUE BVALU 36 50 CCNTJNUE BVALU 37

REIURN BVALU 3« ENU

139

*;./.

Slo COM COM IWBJ

CCM

ISI I CCM

IARL 2,CA

3U. i

LCii C»L QO W( 1 H( 1 M( 1 W(| w( i

M( 1 W(l

10 L< I uc

A* I

If DC lu IF dNL AI AJ I^U JPO IPU IF JPü

QC 20 GO 30 GC 40 GC 90 GC 60 GO 70 GO 80 GC 90 BNu

100 N s DC ir

110 CCN K =

"OUTINfc INTRPL MON// w(2200(7), MON/HNDCRS/ UBT( (7fl|8,7)#pBj(;8, MQN /COMVAL/ KT, OP.üALiKMAX.PORQ HQN /HATVAU *X, .CHAN,ÖMAX.FACT, Y,HDAX.HDAV#DAX2 «EOTM,NI,NJ,NFMA

,NIP?,NTR ICAL AXIS L IPOS^ 10 I « 2.NIM1

L(2200) i09,n,7),PBi(io9.e»iiKn<in9#9), *).JND(7fl>9) AKT.nT.DTMIN^lTER.NEIPRiIPOlNT'.EPR. .PSCL.LR.LF" AY.CFL.VIS.VIST.Mt.VCPHO.XO.PCTO, ANG,AF,SRM,AL.AS.AK,MAL.HAS,HAK,CAL .DAV?.HDAXY,ODAXV,DTR,HALFMU,H.TrHU X,IS.JS,IJSiIBSiISB,JSR.NlHi,NJMl,V

120 K = IF

130 D - AO Al

JS*J.l) • W(IJS* JS*1.2) ■ W(IJS* JSM.3> > -udJS JS*1.4) ■ W<JJS* JS*l.b) ■ W( US* JS*1.6) • -V,(lJS JS*I.7) ■ W(1JS* JS*l) • L(IJS*2* 580 J ■ 2,MJMl ■ IJS*(J-1)«NIP2 S = .FALSE, (j,tQ.2) AXIS 580 I • ?,NIM1 « JJ*l (L(lJ)iNF.2) 50 WY ■ U - FLOAT(I-1)*AX « FLOAT(j-2)*Ay INT = KIJ-NI??) INT ■ IP0INT/9 INT x IP0INT-9*J (AXJS) IPOINT s INT « JP0INT*1 TO (20.230.30,10 TO (220.480,220. TO (470,480,210. TO (300,480,300, TO (100,480,150, TO (470,480,90,3 TO (280,480,28(1, TO (470,480,460, RY « .1 INOMSM,!)

110 K ■ 2,N (AJ.LT.PBKISM, T|NüE N*l K-l (ÖNURY) 190,l3n, PBK lS»I,K)-*j

« AY/(AY-D) ■ 1,0'AO

5*Nir>?*i,i)

• 2*MP?*I,3) ?.MIP2*I,4) ?*NlP2«I.!v) ♦ 2»ixIP?»I,A) ?*NIP2*1,7) MIP2»:)

■ .TRtP,

TO 510

♦ 3*L(IJ«^lP2)*9*LnJ-l)*27«L(IJ*l)

POINT+i o

n,40,50,6C,70,80), IPCINT 150. 420.4C 0,220,530. 220). JPO IM 350.420,40 0,210,530,210). JPOI NT 350,170,300,300,300,300), JPOl^T 350, 42i), i^n, 150,530,150). JPO I NT 50,420,400,90,530,90), JPOINT 350,420,400,280,2^0,280), JPO I »IT 350,420,400,34 0,530.530)1 JPOINT

K) ) GO TO 120

190

INTRPL 2 INTVAL 2 BNUCHS > BNUCHS 3

EPS.EPSl.PDICOMVAL 2 COMVAL 3

XZ,A,B,ABL,nMATVAL ^ ,QAS.OAK,nAXMATVAL 3 ^RTtMU.OOVMMATVAL 4 DiNCl.KP.NElMATVAL •>

MATVAL 6 IMTRt-L 7 IMTWfL H INTRPL 5 IfjTPPLin INTru'Lll IfJTRFLl? iNTOf L13 IMPF-L14 JNTRPLI^1

IHTRPL16 INTPPL17 iNTRPLlfl INTPPLl? INT«?PL20 imprizx INTPFL22 INTRPL23 ^lTRPL24 IIslTBHLi?'' I'^HHZ* IMTRPL27 INT^PLZP IMTBPL29 IMTBPL30 INT3PL31 lNTPPLi2 lMTrPL33 I"TRPL34 I'lTRFL35 INTRPL36 IMTRPL37 iNTPPLje INTPPL39 nTPPL4.' ItgTr?PL4] INTRPL4i IHTRPL43 riTPPL44 HTRPL4,> IMTBPL46 INTRPL47 lNTPPL4fi INTRPL49 IMTRPLSO PJTPPL61

140

DC 140 KK ■ 1,KM*X 140 WtlJ»KK)«*0*WPI<IS*l«K,KKJ*Al»HtlJ*NIP2,KK)

GC TO S7U 150 DC 160 KK ■ IfKMAX 160 H(IJ#KK) ■ W(IJ*NIP?IKK)

QC TO &70 170 DC 180 KK ■ l.KMAX 180 MdJ.KK) » .25«<W(IJ*1,KK»*W(|J.1,KK)*H(IJ*NIP2.KK>»W(IJ

Gf TO &70 190 PC 200 KK « l.KMAX 200 W(UiKK) ■ UBl(IS*I,K,KK)

(iC TO 1»7Ü 210 bKuRY • -I

GC TO J3U 220 BNURY » 1 230 N = IND(IS*1,1)

DC 240 K • 1,N IF (AJ,Lfc,PRI(IS*I,K)) GO TO ?50 CCMTINUE K = N D s AJ-PdI(IS*IiK> IF (BNURV 190,260,320 AO » AY/{AY-D' Al • 1,0-AO DC 270 KK ■ l.KMAX WUJ.KK) ■ Afl*WBI(I^*I.K,KK)*Al«W<lJ-NIP2,KK) GC TO 57Ü DC 290 KK ■ l.KMAX W(1J,KK) = W(IJ-MtP?.KK) QC TO 570 DC 310 KK « l.KMAX WUJ.KK) » 0.5*(^(IJ*NIP2,KK)*W(1J-NIP2.>'K)) GC TO 57U

240

250

260

270

280 290

300 310

320

330

340 350

360

370

380

390

400 410

DZ « AJ-PHI(IS*I,K-1 ) AO « D2/<D2-D) Al » 1,0-AO DC 330 KK « l.KMAX W(IJ.KK) GC TO &70 BKURY ■ -1 N « JND(JS*J,1) DC 360 K ■ 2,N IF (AI,LT,PEJ(JS*J.K)) CCNTINUE K = N*l K = K«l IF (UNURY) 440.380,440 D = PBJ(JS*J,K).AI AO > AX/(AX-D) Al » 1,D-A0 DC 390 KK ■ 1,KMAX W(IJ.KK) GC TO 570 00 410 KK ■ l.KMAx H(1J|KK) » W(IJ*1.KK) GC TO »70

« AO«''lni(IS»I,K.KK)*Al*WPni?*!.K-l.''K>

130 TO 370

« AO^'JfiJtJS^J.K.KKWAl'WC IJ*l,KKt

I*.T I'll INT 1'IT INT INT U:T

•MP2.KK)) INT INT INT INT 1MT I'-lT INT INT 1MT I'.'T [MI

I'MT I'T INT I N T INT I'T I'MT INT I'T l"T irT If T INT 1MT INT

INT INT INT INT INT INT INT P'T INT IM INT INT INT INT I"T I"T INT I'-'T IvT INT INT h'T

BFCll

Rrit»-» 0PLi>') RHLbo WF'Lb^

RKLfc'' DFL6'

ot-Lfc.< kFLfc^ PKL6'' prL6" 3PLft7 '• F 1.6 »■ i FL6V

PFL71 WPL73 RPU7i kPL74 RPL75 RHL76 »PL77 PFL7fl PPL79 RPLB'J RPLHl

RPLÖ.« RPLÖ"

RPLt^ RPLÖ? PPLHH RFLH9 RPL90 RPL95 PPL9i: PPLy3 RPU94 cPL9b

nPL9ft PPL<J7

PPL^fc RPL^y RP10C

RF101 RP1Ü2 RP103 RPIO" r?r lO1? RP1Ü^ WP107

141

i:***».

INTPPIO« 420 DC 430 KK ■ l.KMAX INTRPIU* 430 W(1J,KK) - 0.9.(-(IJ*l.KK)*W(IJ-l.KK>) INTPPUO

UC TO 97U IMTRP111 440 DC 450 KK ■ 1,KM*X NTRP11Ü 490 HtlJiKM ■ WBJCJS^J.K.Kf) HTRP113

UC TO 970 IMTRPU" 460 BNURT ■ -1 I^TRPUb

GC TO 480 I»lTf?Pll6 470 UMJRY ■ 1 IwTRPU? 480 N = JN0(JS*J,1) iMTlvPllf

DC 490 K » 1,N IMTRP11V If (»I,Lfe,PBJ<jS»J.O> RO TO 500 iMTRPir

490 CCNTINUE |»JTRP123 •< = N INTRP122

500 D - *I«PbJ(jS*J.K) IMTFP123 IF (bNDRY) 440,510,«550 MTRP124

510 AO • *X/(*X-D) IMTRPI?"' *1 « l.O-AO lMTRP12t

520 !u!"MK " 1,KHAX • A0.UBJ.JS.J,K.KK,.A1.W(IJ.1..K, j^H^

80 TO !>70 INTRP129 530 DC 540 KK » l.KMAX 1NTRP130 540 W(1J,KK) • W(IJ-1,KK) IMTPP131

QC TO &7ü 1NTRP132 550 Ü2 » Aj-PbJ(jS*J,K-l) INTRPt3;<

AO • D2/(D2-D) I-TPPlJi Al » 1,0-AO 1KJTWP13^

560 Euj"MK " U^ - A0.MHJ(JS*J.K,KK).A1.HBJUS*J.K-1.KK) IMTRPIR

GC TO i70 IN1PH13P 570 COMTJNUF IMTRP135 580 CONTINUE JvTRplAO

DC 600 I B 1#M IKJTRP141 DC 590 J • 2,NJ INTOP142 1J » IJS*«J-1)*MIP2*I IVIRP143

590 L(iJ) « MIN0<L(IJ>.1) 1NTRP144 W(1JS*NIP2*I,3) « 0.0 MTRP145 M( 1JS*NIP2*I,6) ■ 0. INTRPM6 rttUS*l.l) • W(IJS*?.NIP2.1.1» NTRP147 H(lJS*l.Zl • W(IJS*?«N1P2*I,2) lMTRP14fl W<1JS*I.3» ■ -W(IJS*2*NIP?*!;3) INITRP149 W(1JS*1.4) ■ W(IJS*?.N1P2*1,4) MTRP150 W(1JS*1.5) ■ W(IJS*?*NIP2*I.':) ,MTRP151 W(1JS*1.6) • .W(1JS*2*NIP?*I,6) UTRP1Ö2 M(iJS*l./) » W(IJS*?.NIP?*I.71 NTRP1S3

600 L<1JS*1> ■ L<lJS*2«NlP2*n INTRP154 REIURN ISjTRPlSb END

142

10 20

DC 11 12 If UC U

DC U IF

SLbRUUTIhE IPOSN CCtlHÜN// W(?200,7),1.(2200) COMMUN/BNOCPS/ wai(t09,«,7),nPl(109.p)ilND(109.9), lHBJt78,8,7>,pBj(7S,«),JNn(7fl,9) COMMON /MATVAL/ *X,»Y,crL,Vir.VlST,MUYC,PHO»XO.PO, lABL.CHAN.BMAX.FACT.ANQ.AF.Sfl'I.AL.AS.AX.WAL.HA^.HAK, 2.DAY,H0A)(,HDAY,PA)(2.DAY?,HDAXV,0DAXY,DTB.HALFMU.T^T 3UilHfcOTM,NI,NJ,NFMAX.IS,JS.US,IBS,TSB,JSfi.NI Ml, NJM 4,N^NIP2,NTR UC 60 J ■ 2.NJ J4 s tJS*lJ-l)«NlP2 12 » n N = JND(jS*J,l) IF (N.tO.D) Qfi TO 5"

<0 K ■ 2,N,2 « U*X » INT(PBJ<JS*J,K.l)«nAX)*l (u.RT.m no TO 2n 10 I " 11,12 « JJ*l

LUJ) ■ U ii « ia*i 12 • INT(PBJ(JS*J,K)*PAX)*1 IF ( ll.r.T,I2) no TO 40

30 I « 11,12 « JJ*l (KIJl.GT.U GO TO 60

LUJ) ■ Z-LCIJ) CONTINUE CONTINUE II * 12*1 DO 60 I • 11,Nl I- ' JJ*I LUJ) » Q DC 90 I » 1,M Jl » 2 N = INÜ(IS*I,1) IF (N.NE.O) Jl DC 71) J ■ J1,NJ IJ « IJS»(J.1)«NIP2»1

70 L(IJ) « Ü IF (N.LE.l) GO TO 90 K s M DC 80 KK ■ 2,N,2 K = K-2 Jl » 2 IF (K.NE.O) Jl » INT(P3I(IS*I,K)*DAY)*.3 J2 ' lNT(PBI(13*I,K*l)«nAY>*2 IF (J1,GT,J2> GO TO 90 DC 8g J i J1,J2 U = IJS*(J-1)«NIP2*I

eo L(iJ) ■ o 90 CONTINUE

REIURN fcKU

I I B B

TO.XZ,A,P,ABL,DM r.AL.IAS.OAK.DAXM rmuFRTrMu.oevMH 1,ND',NP1.NÜ,NE1M

M

3f 40 50

60

INT(PBI<1S*I.N)*DAY)*3

VAL CHS CCS VAI. VAL VAU VAL VAL SK SK ?r: sr. St

sr

5' 3^ si-, sr SN <?(•(

f Sf. sr SN St. St. Sti SN St SI. sr St-

"f St' SN SN SN SI' •,l. SN SN SI SK SI. SN SN s^ si SN sr SI'

in ii l.' 1' I'' 1'' l' 17 l' i * ^i ?! 2? 2J 2« 2^ 2" 27 2 b 2V 3P 31 3? 63 34 3b 36 37 3« 3^

41 4? 43 «4 45 46 47 Ah 4<S b3 bl

143

»■ i.

10

20

SLbROUTlNh PRNPLT PRNPLT ? CCMMiJN /UNDVAL/ ^.UftOO.7),FRX(6OO),rnY«600),rnS<6li0) BMUVAL 2 CCiMON/StHTCH/ T^R(10ü,7),Trrx<300),'FRY(100) SCHTCH t COMMON /MATARR/ NMAT,IMAT(l?,S),rHAT(23i5>»MAT MATAHR 2 CCMHON /^ONES/ M36G(5.3>,l;EH?(5,3),ARCS!Z<5.3),ri,5M*X(5'.3),0nMlN(Z0NFS ?

iS.o) ZnN,:S 3

CCMMON /CtlMVAL/ KT.iKT.DT.DTl'IM.lTER.NEIpR.IPOlNT.ER^.EPS.FPSl.RDICIMVAL <-

IS. lOP.JAU,KMAX,P0PG.PSCl..UF.Lf DDMmT I XS a l.O/PSCL HRNPLi n YS » XS> PRNPLT 9 CALL P^MT (-XS*PDRG,5,0.-3) PRNPLUn

DC 40 .U1 . l.NMAT noN^TIP

IRb « MATCT.MAT) PRNPLT1J

XO = rMATt9.MAT) nrÄXLT3* YZ=FrtAl(ll,MAT) DrAX ^

X^ * FHArjlS.MAT) PSNPLTU A = FMAT{;3,fAT) o MDi Ti7

b = fMATJ^.MAT) ERNPLTIÖ CHAN = FMAT(17.MAT) PRNPLT19 B^AX • F.IATllB.MAT) KRNPUH>

AN. . FMAKZO.MAT, **ll\]f AF = F*AT(21.MAT) PRNPITP^ DC 10 I « l.NF nrAx 19 ch=rHAM**(eMAX.FRYnRs*n*Yn urAX ,']; TfKVU) . A-B*eC'4-l.Ö>/<CH*l.n) ^ül'.nl"!^ TFNXJl) ■ X0*(FPX(IBS*n-XZ)*ANQ*TFSV(I)*TOP«ATAN»Ar«TFRY(in PRNPLT^5 TFKX(I) ■ XS*TFRX(P PRNPL'Zfc

TFHVMJ » YS.TFPYd) PRNPLT^« CALL PNNT (TFRX.TrRV.3) PB p TV9 Dc 20 ' ' 2'NF no m T^n X = TFHX(l) PRNPLT30

* - ^vlli nzVAl CALL PHNT (X.Y.2) ImlVAl CALL PWNT (TFRX.TrRV.3) ppNPLT34

!0.3?fJ.u?'Nr =";« Y = -TFRY(I)

30 C»LL PHNT (X,Y,2) 40

PRMPLTje

PHNT (X,Y.2> ESLIShl^o ^■i.u rnr»i I »,',<: / PPMP1T38 CONTINUE PRNPUTJO

CALL rHAHt ÄtU' wBlTe ,6(1»0) AKT.KT pp PLTJI «El URN ^T41

50 FCHMAT (1H045X2MT.E12.5,5XM,7H CYCirS/lVl) "^1!' EKU PRNPLT44

144

;,****

SldHüllTIMb PLTQIJT COMMON// -(2200i7»ll(?21C) COMMON /M\DVAL/ wR(Aoo,7),rRX(600)»rPY(*oo),r CCMMüN/SCOTCH/ T»iR<^0U,7),TFrx(S0O),TrPV(30O) CCMHON /M*T*RR/ NHAT.IM*T(12,,S>IFMAT(23,E)»MA

COMMON /ZONES/ NäEG(5.3).NENP(5i3>.*KCSI2(5i3 Ib.o)

CCMMON /ÜOMVAL/ KT.AKT.OT.DTI'IN.ITER.NEIFR,IP lüi inp.UALiKMAX.PORG.PSCU.LFi.Lf

COMMON /MATVAL/ AX,AY.crL.Vir.VIST,Mt,YC,RHO, lAf-L.CHAN^MAX.rACT.ANH.Ar.SRt'.ALtAS.AK^AUHA 2,nAV,HUAX,HnAV,DAX2.nAV?,HDAXY,0D*Xr,DTB,HALF 3Ui IRfeOTM.NI.NJ.NrMAX,IS,JS,IJS.IBS,rSB.JSn.NI 4,IU ,IMIH?,NTP COMMON /TWCPRT/ ^TR<;(5), ITR(r.25)iT'»S(5i?5> bCulV*uFNOE(VZ.T0) UC 60 MAT ■ l.NMAT CALL GtNVAL DO 10 I ■ 1,NF C^ = CHAN*»{BMAX-F9Y( rBS^D^YT) TfKYd) ■ A-B*(rH-i.o)/<ci**i.n) TFHX(I) ■ Xr*(FRX( BS*I)-XZ)*ANO*TFRV(I)«TOP*

10 CONTINUE 00 23 I » l.NTfi j = ITrt{MAT,I) TUi i >RX(IBS*J)*TR«;(MAT,I)*{rRX(lBS*J*l)-FRX TRH i fRY( IRS*J)*TR«;(HAT, I)«(rRY(IBS*J*l)-FRV TWoCl.Z) « WB(IRS*J,2)*THS<MAT,l)»(Mr(lPS*J»l TWrt(I,i) = WB(IDS*J,3)*TRS(MAT,I>*(Wr(IRS*J*l C^=CHA^«»(BMAX-TRR*YZ) TUöd.l) » A-B*(CH.i ,0)/(CH*1.0)

20 Thb(I*i00iU ■ X0»(TRZ"XZ)*Al!f?«THB(I,l)*TOP*A IF (MAT.Ufc.l) GO TO 30 WfilTfcm AKT,NMAr,NFt(TFRX(!).TFRVn),l»liNr)

lThb(l,l),I»l,NTR),(TWH(I,2).TWB(I.3),I«l,NTR) GO Tu «0

30 CONTINUE WfilTfc (?) NF,(TFRx(I),TFRY(I),I ■ l.NFj.MTR.C

1,1 * 1,NTB)I(TWB(I,?>,THB(I,7:),I ■ 1,NTR) 40 CONTINUE

YCM ■ (),99*YC N = 0 00 50 j ■ 2,NJ JJ » IJS*(J-1)«NIP2 DO 50 I « 1,M IF (L(JJ*I),EO.O) GO TO 50 YltLD » W?JJ*I,5)**?*W(JJ*I,6)»«2*W(JJ*I,7)** IF (YIfcLD.LT.YCM) GH TO 50 N = N*l TR^ i UUAT(I-1)«AX TRH s FL0AT(J-2)»AY Ch=CHAN«»(BMAX-TRR*YZ) TFHY(N) ■ A-B*<CH-1.0)/CCH*1,0) TFHX(N) ■ X0«(TRZ-X7)*ANG*TFr,Y{N)*TnF*ATAN(AF IF (N,LT.100) GO TO 50 WRITE (2) N,(TFRX(K),TFRY(K),K ■ 1,N)

r?S«6('0)

T ),niSMAX(5'.3)

OINT.Eor.EPS.

X0,P0, S.HAK, HU,TWT Hl.NjM

TO.XZ.A (:AL,OA«- rMu.rRT

.DISMI

EPSl,R

.R.ABL ,flAK,D CMU.OO 1,NE,N

ATAN(AF#TFPY(I))

HLT I'!l BNU SCK MAT

NCZDN ZON

nionM COM

,PMAT

AXMAT VMMAT ElMAT

MAT TRC UFA PL' PLT PLT OFA PLT PLT PLT PLT PLT

(IRS*J)) PLT (IBS^JJ) PLT ,2)-WB(IPS*J,2)) PLT ,3}-^B(IPS*J.3)) PLT

OFA PLT

TAN(AF«TWB(I.1)) PLT PLT

,NTR,{Twnn*tno,i», pi.T PLT PLT PLT

TWfl(!*10n,l).TWBtI,l)PLT PLT PLT PLT PLT PLT PLT PLT PLT

2*W(JJ^I15I«W(JJ*I,7)PLT PLT

PLT

PLT

PLT OFA

PLT

•TFRV(V>) PLT

PLT

PLT

DI.T ?. VAL ^

VAL '■>. TCK ■•,

AhP 'S

es ■' ES

VAL

VAL VAL

VAL VAL

VAL ■' VAL fr PHT ?

X 4;

niJTU nuna OLTIJ X 41 nLTl5 0LT16 nuTi? OtTlH nbTi« nUT2Ü nUT21 0UT22 nUT23 X 4? ruiT2t> 01IT26 niTz? lUTZfl nuTii? 0UT3R OI.T31 nijT32 nlJT33 ni)T34 niJT3tj

nUT36 0UT37 nuTje riL1T39 nUT40

01JT41 nUT42

DUT43

nUT44

nUT4b X 43

nijT47

nuT4fl nLiT4<>

nUTSO

145

iffi/Mif

N - 0 90 CCNTINUE

HfilTt (2) N,(TFRX(K),TFRY(K),K ■ 1|N) 6(1 CCI\T1N0E

HEIURN fc\U

PLTnUTSl PLTOliTb2 PLTmiTSi PLT0UT&4 PLTOl'TSti PLTOtiTb*

146

t'JjSik-f:

SLbHOUTINt OUTPUT ?J,TUAI ?

CChMON/HNUCRS/ WBI<lO9.«,7).Pni(lO9,e>,IND(109,9), BNUCHS Z

COMMON /BNDVAL/ WR(AOO,7).rRX(600),rnY(600).rRS<600) 8MUV*L 2 COMMON /MiURP/ NMAT,IM*T(1?,5),FMAT<23,5)»MAT „«ITWAI ? COMMON /M*mU *X,4V,CrL.VIS.VlST,MU.VC,RH0#X0.P0,T0.XZ,*,P.*BL,DMATVAL Z

lAPL.CHAN.riMAX.FACT.ANG.Ar.SBH.AL.AS.AK.HAL.HAS.HAK.RAL.BAS.OAK.OAXMATVAL J 2.CAy,HDAX.HnAV.DAX2.DAY?.HDAXY.QDAXy.DTR,HAI.rMy,TWTrMU.fRTCHU.00VM^ 4 3UiIRfcOTM,Nl,NJ,NFMAX.IS.JS,!JS,IBS,lSB,JSP.NIMf..NJMl,ND.Nnl,NE,MElMATVAL i

4CCMASiP/^i[Js/ ISTART.TMAX.TPRIN,TPRPL,TPLOT,TSAVE,TCnMP.TZ TVALS ? COMMON /THCPRT/ NTR«;(5),lTR(r.29).TR«(5,25) „„.I'MW., N COMMON /COMVAL/ KT.AKT.DT.DTMIN.lTER.NEIBP.IFOlNT.EPP.EPS.EPSl.RDICnMVAL ,

iS.IOP.UAU.KMAX.PORG'.PSCL.LP.Lf "^*L t COMMON /i'Urc/ MNFr.INFC(60>.NONlN(20.9) ^JJ' ': COMMON /PRESS/ PDER.PR.PE.HATNO ^" ^ DIMENSION WCUT(8) "^I L fcCUlVALENCE(YZ,TO) ^T^ ^

t;foSt-R^CHAN..(BMAX.Y*YZ)-1.0>/<CHAN*.(BMAy-Y*YZ)*1.0) OFAX ^ Z(X.Y) » X0*(X.XZ)*ANC«Y.TOP*ATAN(Ar.Y) ^^T 1«

PCtR « .MLSE, ßl, I :. DO 100 MAT ■ i.NMAT VJV\ :c IPK1NT . IHAT(ll.MAT) "1 ' * JPrtlNT = IMAT(12.MAT) SJui ji IF (MAT.NE.D GO TO 10 "^; ;* CAUL SfcCOND (TD "vy ' RT - H-TZ 0\l 24 WRITE C6,170) AKT.DT.KT.RT "j^ f, GO TO ^0 ",' y6

10 WRITE (6,130) MAT ü ' ' <:_ 20 CALL_ GfeNVAL r?-»'' 27

WRITE (6.120) l - ZC1N = 1,0E6 QTH ' 30 RM1N = ZMIN Ul Z^AX » -Z^IN °T(,; ja RKAX » 7MAX ^l " DC 40 ! . l.NF ?!JJ I] ZKIN = AMIN1(FRX(IBS*1>.ZMIN> °;^ ' ZMAX ■ AMAXl(FRX(IBS*I>.ZMAy) ^^ ^ RMIN s AMlNKFRYdBS^D.RMlN) ";;' *'l RMAX « AMAX1(FRY(IB«!*I).RMAX> ^ \ RR = RIFRV(IBS*I)) "'^1 :,, ZZ » Z(FHX(IBS*I).RR) n'p' I. DC 3o «K . 1,7 ;^T ;;

30 WCUT(KK) • WB(IBS-l.KK) "jrL " WOUT(fl) « PRS(WOÜT(l).WOUT(4))*P0 ^^ ^ WCUTH) 1 WOUT(l).RH0 U .. WCUT(5) ' WOUT(5)*P0 (,TuT 45 WOUT<6) • W0UT(6)*P0 UJy W0UT{7) 1 W0UT(7)*Pn niHT «7

40 WRITE (6,140) I.ZZ.RR.WOUT " ^ ' IF (IPHINT.EQ.0.0R..lPRINT.EO.n) GO Tr 7C OTHT «e IB » INT(ZMIN*DAX)*? "IpT =, IE « INT(ZMAX*DAX)*1

147

IF (IPKINT.GT.O) IE « MINÜ(ir*lPRINT-l,IE> 0THT b7 IF (IPWINT.UT.O) IB » MiXO(lE*IPRlNT*l,IB) 0TPT 5,3 Jp « 1^T(HMIN*D*^»*' OTHT 5« jt » I'Tt«MAX«D*n*3 0TpT ^

IF (JPHINT.LT,0) JB » M*XO(jr*JPRINT*l,JB) 0TpT ^ WhlTt (6il50) OTHT 6^ DC 60 J ■ JB,JE OTPTCl 1 WSlTb(Ö.l^O) J OTPT V' HK " PCFL0AT{J-2>«Ay) OTPT Mi Jw ■ lJS«(J-l)«Nlp2 OTHT 61 UC 60 I ■ IP.IE OTPT 62 IF (L(JJ*I),EQ.O) GO TC OO 0THT 6J 11 ■ Z(FLQAT(1-1>*AX,RH) orHT 6^ UC 50 KK « 1,7 OTPT 65

50 WCUT(KK) • W(JJ*I,KK) 0T(JT bt WCUT(Ö) ■ PRS{WOÜT(l),w1UT(45)«P0 0TPT 6? WCUT(I) ■ WnuT(l)»RM0 OTHT 6« *CUT(5) • W0UT(5)*Pn OTPT 6'' WCUT(6) • WOUT(6)*P0 OTHT 71) WCUT(7> ■ WOUT<7)*Pn OTPT 71 wRiTfe (6.140) I.ZZ.RR.^UT 0TpT 72

60 CONTINUE OTPT 73 70 wBlTt (6,160) OTPT 74

DC 90 1 » l.NTR OTHT 7b m iT";nBsij)*TR.<MAT,n.(rRx<iBs*j*i>.rRX(iBs:j)) OTHT 76 TRH > FRY(IBS*J)*TR?(HAT.!).(rRV(tBS*J*l)-rRV(IBS*J)) OTPT 76

„ SSU?!K" : Ä^.-T.S-.'.T ..„^.i.KK.-uR.ns.j.««.. S;j; j; RR ■ RUHR) OTHT 61 11 • Z(THZ,RR) , ,, „„ OTHT »2 H0UT(8> ■ PRS(W0JTM),WOUT(4))«P0 0TpT fi3 WCUT(I) ■ WOUT(l)«RM0 OTHT 84 WC0T(5) ■ WOUT(5)«P0 OTHT 85 WCUT{6) • WOUT(6)«Pn OTHT 86 W0UT{7) • WOUTt7)*P0 OTHT 87

90 NR1TE (6|140) I.ZZ.BR.WOUT 0TpT bS

100 CONTINUE OTHT b? DO HO I ■ l.NINFC OTHT 90 JE • 6«I OTHT 91 JB ■ J6-& n ir,4 OTPT 92 WRITE (6.180) (INFC(J).J ■ JP.JE) 0TPT 93 RETURN OTPT 94

110

t20 FCHMAT (IMO/5H0 PT.6XlHZ9XlHn9X3HRMOllXlHUl2nHV17XlHEllX3HSZZ10X3^^ »

5 - OTPT 97

130 FCHMAT (lHl//5ex8HM*TERIALl2> OTPT 98 140 FCHMAT (J9,2ri0.*.8^13,5) OTHT 99 150 FCHMAT (IH0/55X15HINTERIOR P£JNTS) 0TpT l0C 160 FCHMAT (1H0/54X16HTPACER PARTICLES) CYCLES5X13HELAPSE0 TIMOTPT 101

148

:■&:■$■... äx&m

2TEKIAL 1> 0TPTC1 7 ISO FCNMAT (»H0M*TEBULt2illH FROM P01NT|4,9H TO P0INTI4,31H HAS *N INOTKT 103

lTEHr*rfe WITH MATERI*LI2»11H FROH P0INTI4,9H TO POtNTJ«) OTPT 104 190 FOHMAmH059Xl3) OTPTC1 H

EKU OTPT IDb

149

SUflRUUTINF SAVE COMMÜfJ/V W(2200.7t,LJ22Un) COMMON /dNDVAL/ WU(600,7),rRX(600).rPY(600),FHS(60 COMMUN/SCRTCH/ Thn<Jon,7)lTrhXM0O),TrRY(3O0> COMMON /ZONES/ NBECt5i3),NEN0(5.3) . A8CSIZ(5.3>.MS

19.3) COM'IUN /M*TARR/ NMAT»IMAT(12,5),FMAT<23I5).MAT

COMMON /COMVAL/ KT,AKT,nT.DTMIN, I TER.NEIB«. !POlNT, IS.TOP.LAL.KHAX.POHC.HSCL.l.b.Lf

COMMON /T9CPRT/ NTRSC), ITR (3, Z'J ). TBS (5.25 ) COMNON /IMTrc/ NlNFC.lNK(oO).UÜNIM20,9) HEwlNO 1 hRJTb 11) KT.AKT.nTMl'l MN* = 6*MlNFC WRlTb <1) NINrC.NIN6.(rTr(I),I « 1,MN6) DO 7U MAT « l.NMAT MR » MTHS<MAT) rT ■ iJfeNÜ(M4T,3) MI ■ IMAT(l.rtAT) NIP2 » NU2 JJS ■ I^AT<«,MAT) IMS ■ IMAT(7,MAT) AX ■ FMATd.MAT) IJAX « 1,0/AX AViFMAKZ.iiAT) DAY»1,Ü/AY YZiFMAT(ll.MAT) XZ * FhAT(l2,MAT) ZMJN ■ 1,0E6 KMIN B ZMIN ZMAX » -ZMIN HMAX e ZMAX BO 10 I ■ l.NF ZMIN ■ AMIN1(FRX(IBS*I>.ZM1N> JMAX » AMAX1(FRX(IES*T).ZMAX) RMIN ■ AMINl(FRY(ieS*I>iRMIN>

10 «MAX « AMAX1(FRY(IES*I).RHAX) IB.INT<ZMIN«DAX)*2 IE>INT(ZMAX«DAX)*1 JB«INT(RM1N*ÜAY)*3 |F(RMIN,|.E,1.0E-4) JB»1 JE«INT(RMAX«DAY)*2 NI « 1E-1B*1 NJ ■ JE-JB*1 ZPF « FLOAT(l-IB)»*X XZ » XZ*ZDF RDF»FLOAT(l-JB)*AY YZiYZ*RDF DO 20 I ■ l.NF TFRY(I)«FRY(IPS*I'*RDF

20 TFRX! I) ■ FRX(IBSM)*ZLF hPlTfc (I) (MaEa(MAT,I).NENU<MAT,l),AfiCSIZ(MAT.I),

l.NF.VZ IT1»IBS*1 |T2»IBS*NF «RlTfc(l) ({UB(I,KK),KW«l,KMAX).rHS{n.I«ITi,lT2j,

SAVE ? I'lTVAl 2

0» rf^DVAL 7 SCRTCH ■>

MAXdJ.SJ.TlSMINtZ^NES ? ZONES \ MATAHR 2

ERR.EPS.EfSl.RDlCIMVAL ■)

C.IMVAL 3 Tt>CPRT 3

IMTFC ■>

SAVt 11 SAVF 1? SAVfc n SAVE 14 SAVH 15 SAVf: If SAVE 17 SAVE 11 SAVE 19 SAVE 20 SAVE 21 SAVE 22 SAVE ^^ OFAX 46 OFAX <7 orAX 48 SAVE 25 SAVE 26 SAVE 27 SAVE 25 SAVE 29 SAVE 3n SAVE 31 SAVE 32 SAVE 33 SAVE 34 SAVECl 1 SAVEC1 2 OFAX 49 OFAX 50 SAVECl A SAVE SAVE SAVE SAVE OFAX OFAX SAVE OFAX SAVE

I • 1,3),X7.M.NJSAVE OFAX 54 SAVECl 6 SAVECl 7

(TFRX(1),TFRV( I),SAVr:Cl 8

150

f

k-RlTfc (i) NTR.(jTR<M*T,n,TMS<MAT.I),I ■ l.NTR) DO 2* J«JB,JE JJ»tJS*<J-1)«MIP2

IT2»JJ*IE 25 NRlTkU> ((b(I>KK),KK-l,KHAX).l.(I)>IalTi«IT2) JO CONTINUE

iND FILE l RRTURM fcND

S*vKCl 3 S*Vf *" SAVEClin SAVfeClll S*V6Cll2 SAvecm S4W^C114 S*VE 62 S»VE 5S SAVE t>4 SAVE fes

151

&uäi

SLbHüUTINfc FRAME COMMON /COMPLT/ IXO.IYO.IXN.IYN.IPEN.IMAX.JM

IG.XS.YS DIMENSION L(121)i lrH*R<37) LOUICAU IPEN.FLAG OA1A IdLNK/lH / DAU ICHArt/lH*,lHA#1HB,lHC.lHD.lHEilHr»lH0.1

l.lMN.lHOilHP.lHOilHP.lHS.lHT.iHU.lHV.lHWjlHX

MRITE (6(!>0) N - X JT ■ IMAX'JMAX OC 30 I « l.IMAX JT ■ JT-JMAX UC 10 J ■ l.JMAX

IT L(J) * löLNK 20 MN ■ M(N)/64

IF (MN.LT.JT) GO TO 3ü jj ■ MN-jT K = M(N)-MN*64 L(JJ) ■ ICHAR(K*1) H s N*l IF (N.UE.NP) GO TO ?0 wKlTE (6.t0) L ÜC TQ 40

30 WRITE (6,60) L 40 CALL RESET

RE i URN

50 60

FCHMAT FCNMAT fcKU

ani) (1H .121A1)

FPMP 2 AX.NP'.MAXI'.HCPOOOJ.FUAFRME i

FRME 4 FRME 5 FRMP 6 FRME 7

HH.IHMHJ.IHK.IHL.IHMFRME H ,1HY,1H7,1H0.1HI,1H?.1FPME 9

FRMg 10 FPMF 11 FPMF. U FRMF 15 FPMP 1" FBMc l^ FRME 16 FPMg 17 f PMF lw FPMF 19 FRMC 21) FRME 21 FRME n FRMF 2i FRME 24 FPMF 2b FRMF 2ft FRMF 27 FPMF 2H FRMF 29 FPMF JO FRME 31 FRMF ■S2 FRMF 33

152

'

■ tahC

SLHHOUIINfc C*LL PfcSfcT

HtIUHN

PRUTS (N.K) PUTS 2 PLTS 5

PLTS " PUTS b

153

*>itä&

IGiXS.YS RekT ■, LCüICAL IPEN.riAG R^; ft

IXU - 1 RStT 7

R«;tT H RStT 9 RStT 11 RStT 11 RStT 12 RStT 1^ RStT 14

IVU ■ 1 |XN ■ 1 1VN ■ 1 IPcN » , THUF. FLAG » , TRUE. NP » 0 REIUHN fcNtl

154

/ y y ID )

IX0.1Y0.1)(N,iyH,IPEN,lHAX,JMAX,NPiM*X»»,

■ inxtxs*x)*jxo ■ IFIX(YS«V)*1V0 « JP <UdS{IP).E0,2) IPPN » .rnuE, (I»ÜS(IP).E0,3) IPEN ■ .FALSE, «,NOT,IPEN) GO TO 40 » MJNÜ(IY,IYN) ■ M*X0«IY,IYN) » MINOdX.IXN) « MAXU(IX,IXN) df^T, IMAX,Ci?,lL.LT,1.0H,JF.OT,Jf'*X.CP.JLiLT,l) GO

iUbRQUTINt PRNT COMMON /COMPLT/ iGiXSiYb LOUICAL IPEN,Fu*0 IX P IP IF IF IF IF IU JF JL {F » 1 r , u i e s i'' Cx a JX-IXN ICY • lY-IYN IF (lAdS(IDX),GT, lABSUDY)) 00 TO 20 IF UDY.tQ.O) GO TO 40 IF « M*XO(IF,1) IL » MINOCIL.IMAX) DC 10 I ■ IF.IL J = IXN*(IDX*(I-lYN))/inY IF «J.LT.l.OR.j.GT.JMAX) GO TO 10 C*LU StTPT <I,J,0) IF ( ,NOT,FLAG) GO Jr 40

10 CONTINUE GO TO 40

20 CONTINUE JF ■ MAXÜ<JF,1) JL « MlNO<JL,JM*X, DC 30 J ■ JF,JL I = IYN*(IDY«fJ-IXN))/inx IF (l.LT.l.OR.I.GT.IMAX) GO TO 30 CALL SbTRT (I.J.O) IF (.NOT.FLAG) GO TO 40

30 CONTINUE 40 IXN ■ IX

IYN ■ IY IF (IP.GT.O) RETURN IXU a IXN pu a JYN REIUHN ENU

PRrjT 2 H{2000)|F-L*PPNT .5

PRNT 4 PRNT t> PRNT ft PRNT 7 PRNT h

PRNT 9 PPNT 10 PRNT n PRNT 12 PRNT 1-5 PRNT 1" PRNT I1*

TO 40 PRNT 15 PRNT 17 PRNT lu PRNT 19 PPNT W PRNT 21 PRNT Ü2 PRNT 23 PRMT 2" PRNT 2b PRNT 26 PPNT 27 PRNT 26 PRNT 29 PRNT 30 PRNT 31 PRNT 32 PRNT 33 PPNT 34 PRNT 3b PRNT it PRNT 37 PRNT 38 PRNT 39 PRNT 4n PRNT 41 PRNT 42 PRNT 43 PRNT 44 PRNT 4'»

155

_1.— _.-

SLdROUTINt SETPT t I.J. ITHR) COMMON /COHPLV IX0.IVO.IXN,lVN,IPENlIMAX,JMAX,Np;M*XP,M<2000).fUASTPT

1G|XS,YS LClilCAL IPEN.FLAG N « (JM*X*(I-1)»J)«64 CALL SEEK (M,NP,N,K)

TO 31

?D

IF (K.UT.O) RETURN NP » NP*X IF (NP.GT.MAXP) GO K s »K*! IF (K.ÜT.NP) GO TO LL » NP DO 10 L ■ K.NP LL » LL-1

10 M(LL*1> ■ M(LL) 20 M(iV«l) » N«.1CHR

HE I URN 30 NP ■ NP-1

IF (FLAG) WRITE (A FLAG ■ .FALSE, RElU^N

,4Ü) NP

40 FCHMAT (1H1///25H0ATTEMPT TO SET MORR THANI6,3aH PRKT POUTS, lIMNü POINTS IGNOREn)

STPT 2 .FLASTPT 3

STPT 4

STPT 13 STPT 6 STPT 7 STPT H STPT 9 STPT 10 STPT 11 STPT 1? STPT Ü STPT 1« STPT 15 STPT 16 STPT 17 STPT IP STPT 19 STPT iJ'l STPT 21 STPT 22 STPT 2i

RfMASTPT 21 STPT 2!) STPT 26

156

CcS'/SoMpCT^uSl^O^UNliyN.lPEN.IMAX.JMAX.NPiM^.HCjOOOJ.FLASMbu

lüiXS.YS LOülC*L IPEN.FLAG IXN ■ IFIX(XS«X)MX0 IYN • inX(VS«Y)*IVO IF (IXN.UT.I.OR.IXN.GT.JMAX.OR.IYN.LT.J.CR.IVN.GT.I^AX) RETURN

CALL StTPT (IVN.IXN.ISYMB) KElÜRN

SMbL ? SMbL 3

SMHL A SMBL h

SMbL 6 SMbL 7

SMöL (' SMbL <5

SMbL li: SMbL 11

157

10 20

30

40

50

60

70

ao

90 100

SlöROUTINfc SEEK U,wP.PP,K) OlnENSlON A(l) IMEÜEH AiP.PP IT ■ NP IF (JT.FO.O) GO TO ^0 18 ■ 1 p s pp IF <<P-*(l>)/64) 10,20,30 IF ((P-A(lT))/64) 40,50,60 I * 1 GC TO 10Ü I * -1 GC TO 10Ü I * -IT-l ÜC TO 10« 1 - IT GC TO 10U IF ( IT-Id,E0.1) GO TO 90 I = Ud*lT)/2 IF {(P-A(I))/64) 70,100,80 IP ■ I GC TO 60 IT » I GC TO on I = «IT K = I RE HIHN

SEtK 2 SFtK ,5 SFtK 4

SEtK b SEEK ft SEtK 7 SEEK Ö SFtK 9

SEtK 1" SEtK H SFtK U SEEK 13 SFtK 14 SEtK lb SFtK 16 SEtK 17 SFtK IS SEtK 19 SEcK 'iii SEtK ?.x SEtK 2? SEtK 23 SEtK 24 SEtK Z^ SFbK 26 SEtK 27 SEtK 2« SEtK 2«

158

WM—wj

«LUCK U*T* ÖK1JT ü CCMMQN /COMPLT/ IXO.IYÜ,IXN,1VN,IPEN,IMAX.JMAX#NPIM*XP.H<!)000).FL*BKUT 3

IG.XS.YS ÖKUT ->

D*IA IM*XiJMAX,M*XP/61»121»?CO0/ H,<UT ' Ü*l* XS.YS/10,0001,6,0001/ ÖKUT o tNu BKUT /

159

V

fUNCTION PRS (RHOO.FE) P»S ? COMMON /PHESS/ PDFR.PR.PE.MiTNO PRfcSS i COMMON /EOSTP/ *PL(lO)iHPL(lO).*PB<lO)i0PR(lO>.*LPH(in);BFT*(lO).EEQSTP 2

lS<10),bZfcHO(lO),ESPRM(10),RHn2RO(lO),P*IM10) EOSTP i LCUICAL MlN PBS b LOGICAL PDER PRS h REAL MU PRS 7 D* I A APl..aPL,APB,pPP,A|.PH,EE"pA#RHO2RC.EZEROiE5,f;SPRK,PM|N/0,5,0.5,PBb e

10.3.0.3.ü.5,O.OiO,O.O.O.C.O.C.O,1.50,l,n4,1.50,1.10.1.63,0.0,0.0,npnb Z.O.O.OiO.O.J.JB.S.O«.!.?«!.068,0,75,0,0.0.0.H. 0.0 ; 0.0.0.1. 09,2.50,PRb I'l 31.05,0.04.0.65,0,0,(1.0,0.0,0.0.0,0,5,0,10.0,5.0.5". 0,'5.OiO.0.0.0.0,PHb 11 40iU,0.0.0.6,0.10,0,5,0.5.0,5.0,0.0,0,0.0.0,0,0,0,0,7,9,17.04,8,O.lPRü 1? 5,6V4,2l7V.0,0.0.0.OlO.O.0.O.r.O,095.(),225,0,0''5,0;Oft0.0:O5.O,O.0,0PBS Xi 6,0.0, 0,0,0.0.0,0244,0,0111,0.0244,0,0 320,0.03, 0,0, 0,0,0.0.0.0.0,0,PRS I4

70, i 02, ü. 056, 0,10 2, 0.180, 0.15, U, 0 »0.0, 0,0, 0.0, 0.0,. 0.0 35',-0,0 0371,-PRb l"5

80,035.-0,0033.-0.035,0.0,0.0.0.0,0.0,0,0/ PRS 1^ C HATUJ'TAROET, MAT(2)«PROJ , MAT(3)«PRnj SHEATH PPS> 17 C PRb li:

MAI ■ MATNO PpS 1« ETA ■ HHOO PPS ZU IF (ETA.üT.0.0) GO TO 10 PRS 21 fcTA ■ -ETA PRb 22 MtN ■ .FALSE. PfS 23 GC TO 20 P^S ?4

10 MIiN » ,THJE. P^S ^^ 20 CCNTINUE PBS üh

E = EE PPS 27 R = fc-5A«RHOZRn(MAT) PPS 2H ML s ETA.1.0 PRS 2<5 irsÄc(S(MU'.LT,l,OF-(i) iinn.o PRS 3n E- ■ (-.•iL(MAT)/(E/(E7ERÜ(MAT)«FTA**2)*l,0) PRS 31 IF (fcTA.Ufc.l.0.OR,E.Lt,FS(H*Tn GO TT 30 PRS M IF <E,GE.eSPRM(MAT)» r,0 Tfl 50 pi'S 33

C PPS 34 C CUMPRfcSSlON PRS 35 C PRb 3ft

30 PRSC « (APL«MAT)»FX»*E*R»(APn(MAT)*BrB(KAT)*^l)*M(J PRS 37 IF (MlN) PRSC « AMA)(l(PMSr,PHIN(MATn PRS 30 IF (,NUT,PDER) GC To 40 PpS 39 PRL ■ (APL{MAT>«E*)«E*(APP(MAT).2,0*RPB(|'AT)«MU)/PHrZRO<MAT)*2l0*(PRb 40 :E*tX/ETA)»«2/(EZER0(MAT)«PPL(MAT)) PRS 41 PEL ■ (APL(HAT)*E)(-F«(EX/'ETA)««2/(EZER0(MAT)*BPL(MAT)))*R PRS 4?

40 IF (ETA.LM.0,ANn.F,OT.FS(MAT)) GO TO !C PPS 43 PRb ■ PRSC/RHC2R0(MAT) PRS 4* IF (,NUT,PDER) RETUPN PRS 45 PR ■ PHC PPS 46 PE ■ PfeC/HHOZRO<*AT) PRS 47 REIUHN PRS 48

50 EV » EXP(-ALPH(MAT)«(MO/ETA)««2) PPS 4V EZ ■ EXP(HETA(HAT)*MU/ETA) PRS 50 pfibE » APL(MAT)»E»R*(E*R»FX*APb(MAT)»ML»F7)»EV PWS 51 IF (MIN) PRSE « AMAX1(PRSF,P>,IN(MAT)) P^S 52 IF (.NQT.PDFR) r,3 TO 60 PRS 53 PRt ■ APL(M*T)*E«((F»R«F)(*APn(MAT)«ML*EZ)«2,D»ALPw<^AT)«Mu/(P*ETA*PRb 54 l*2)*E*6X*i.Q»(E»Ev/PTA)*.2/(r7ER0(M»T)*PPL(MAT))*(APB(MAT)/Ph0ZR0(PRS bb 2MA1 )*ApB(MAT)*MU»RfcTA(MAT)/(rTA«R>)«"Z)»FV PRb 66

160

Pfet ■ UPI.(MAT)*(EX-EMEX/FTA)««2/<EZER0(MAT)«BPL<MAT)n*FY)*R 60 IF (E,LT.ESPRM(«*T)) r,0 TO 7C

Pfiä ■ PRSfc/RHOZR0(M»T) IF (,N0T,PDER) RETURN PR s PHE Pfe « PEE/HM02RO(M»T> REIURN

70 A = (E-Eb(MAT))/(ESPRM(MAT)-E9(HAT)) B s (FSPRN(MAT)«E)/(ESP»»M(MAT)-BS<MAT)) PHs ■ (*«PRSE*B*PPSC)/''^02R0<MAT) IF (.NUT.PDER) RETURN MR i A*PRfe*B«PRC PF. ■ (A*P6E*B«PEC)/RH0ZH0(MAT) RE I URN

PRb t)7 PRS 6H PRS s« PRb 60 PRS 61 PRS 62 PRb 63 PRb 64 PRS 6b PRb 66 PRb 67 PRS 6b PRb 69 PRb 70 PBb 71

161