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Introduction to MIKE 11 by Bunchingiv Bazartseren. Cottbus May 22, 2001. Outline. General Hydrodynamics within MIKE 11 flow types numerical solution Modelling with MIKE 11 Example demonstration input preparation simulation visualization. General 1. 1D flow (wave) simulation - PowerPoint PPT Presentation
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Introduction to MIKE 11
by Bunchingiv Bazartseren
CottbusMay 22, 2001
May 22, 2001 Introduction to MIKE 11
Outline
• General
• Hydrodynamics within MIKE 11• flow types• numerical solution
• Modelling with MIKE 11
• Example demonstration• input preparation• simulation• visualization
May 22, 2001 Introduction to MIKE 11
General1
• 1D flow (wave) simulation
• Application into water system• for what purpose?
• design• management• operation
• where?• river• estuaries• irrigation systems
May 22, 2001 Introduction to MIKE 11
General2
• Main modules • Rainfall-runoff
• NAM, UHM• Hydrodynamics
• governing equations for different flow types • Advection-dispersion and cohesive sediment
• 1D mass balance equation• Water quality
• AD coupled for BOD, DO, nitrification etc• Non cohesive sediment transport
• transport material and morphology
May 22, 2001 Introduction to MIKE 11
Saint Venant equation1
• Unsteady, nearly horizontal flow
0
q
2
2
ARC
QgQ
x
hgA
x
AQ
t
Q
t
A
x
Q
where , Q - discharge, m3 s-1
A - flow area, m2
q - lateral flow, m2s-1
h - depth above datum, m C - Chezy resistance coefficient, m1/2s-1
R - hydraulic radius, m -momentum distribution coefficient
May 22, 2001 Introduction to MIKE 11
Saint Venant equation2
• Variables• two independent (x, t)
• two dependent (Q, h)
• Conditions for solution• 2 point initial (Q, h)
• 1 point up/downstream• h
• Q
• Q=f(h)
May 22, 2001 Introduction to MIKE 11
Flow types
• Fully dynamic
02
RAC
QQggAi
x
hgA
• Diffusive wave - no inertia
• Kinematic wave - pure convective
0
ix
h
May 22, 2001 Introduction to MIKE 11
Finite difference method
• Discretization into time and space
t
xx
t
x nn
1
Difference between explicit and implicit scheme
May 22, 2001 Introduction to MIKE 11
Solution scheme1
• Structured, cartesian grid• Implicit scheme (Abbott-Ionescu)
• Continuity equation - h centered• Momentum equation - Q centered
j
nj
nj
nj
nj
x
QQQQ
x
Q
222
1111
11
Example discretization:
May 22, 2001 Introduction to MIKE 11
• Transformation into linear equations
Solution scheme2
jnjj
njj
njj
jnjj
njj
njj
DhCQB1hA
DQChBQA
111
111111
111
11
111
jnjj
njj
njj DCBA 1111 1
111
1
• Tri-diagonal matrix form of equation
A0 B0 C0
A1 B1 C1
A2 B2 C2
. . . . . .
Ajj Bjj Cjj
0
1
2 . .
jj
D0
D1
D2 . .
Djj
n+1 n
=.all zeros
all zeros
(mass)
(momentum)
May 22, 2001 Introduction to MIKE 11
• Less equation than unknowns • Use of suitable boundary conditions• Introducing additional variables
Solution scheme3
• Substitution of into the linear equations
• Derivation of recurrence relations
jjj
jjjj
jjj
jj
BEA
CADF
BEA
CE
1
1
jnjj
nj FE
111
May 22, 2001 Introduction to MIKE 11
• Double sweep algorithm• calculate the coefficients A-D• obtain Ejj, Fjj from right hand boundary
• sweep forward to calculate Ej, Fj
• sweep back to calculate jn+1 for all grid
Solution scheme4
May 22, 2001 Introduction to MIKE 11
Network of open channels1
• Use of graph theory • Set of vertices and edges
• edges - channels • nodes - river confluence
May 22, 2001 Introduction to MIKE 11
• Incidence matrix from the network
• Confluence nodes - h boundary
• Each channel - diagonal matrix
• Consideration of lateral flow
Network of open channels2
1 11 1 1 1 1 1 1 1
edges
nod
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