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MIKE 11 IntroductionNovember 2002 Part 1

Introduction to MIKE 11

Part 1

General

Hydrodynamics within MIKE 11

Basic Equations

Flow Types Numerical Scheme

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MIKE 11 IntroductionNovember 2002 Part 1

General

Simulation of 1D Flow in

Estuaries,

Rivers and

Irrigation Systems, etc.

Application for Inland Water System Design,

Management and

Operation

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MIKE 11 IntroductionNovember 2002 Part 1

Main Modules

Rainfall-Runoff

Hydrodynamics

Advection-Dispersion and Cohesive Sediment

Water Quality

Non Cohesive Sediment Transport

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MIKE 11 IntroductionNovember 2002 Part 1

Basic Equations

Assumptions

Constant Density

Small Bed Slope

Large Wave Length Compared to Water Depth

Uniform Velocity over the Cross Section No Vertical Acceleration

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MIKE 11 IntroductionNovember 2002 Part 1

de Saint Venant Equations

(Mass and Momentum Conservation):

0

q

2

2

=+

+

+

=+

ARC

QgQ

x

hgA

x

A

Q

t

Q

t

A

x

Q

a

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-1R - hydraulic radius, m

a- momentum distribution coefficient

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MIKE 11 IntroductionNovember 2002 Part 1

Variables

Independent variables

space x

time t

Dependent variables

discharge Q water level h

All other variables are function of the

independent or dependent variables

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MIKE 11 IntroductionNovember 2002 Part 1

Flow Types

Neglect first two terms

Diffusive wave ( backwater analysis)

0

2

2

=++

+

ARCQgQ

xhgA

xA

Q

tQ

a

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MIKE 11 IntroductionNovember 2002 Part 1

Flow Types

Neglect three terms

Kinematic wave (relatively steep rivers

without backwater effects)

0

2

2

=+

+

+

ARC

QgQ

x

hgA

x

A

Q

t

Qa

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MIKE 11 IntroductionNovember 2002 Part 1

Finite Difference Method

Discretisation in time and space

t

xx

t

xnn

D-

@ +1

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MIKE 11 IntroductionNovember 2002 Part 1

Numerical Scheme

Equations are transformed to a set of

implicit finite difference equations over acomputational grid

alternating Q - and h points, where Q and h

are computed at each time step

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MIKE 11 IntroductionNovember 2002 Part 1

Numerical Scheme

Example of discretization

( )( )

j

n

j

n

j

n

j

n

j

x

QQQQ

x

Q

2 22

1

1

11

1

1

D

+-

+

=

-

+-+

++

Implicit Finite Difference Scheme (Abbott-

Ionescu) Continuity equation - h centered

Momentum equation - Q centered

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MIKE 11 IntroductionNovember 2002 Part 1

Boundary Conditions

Boundary conditions

external boundary conditions - upstream anddownstream;

internal boundary conditions - hydraulic

structures ( here Saint Venant equation are notapplicable)

Initial condition

time t=0

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MIKE 11 IntroductionNovember 2002 Part 1

Boundary Conditions

Typical upstream boundary conditions

constant discharge from a reservoir

a discharge hydrograph of a specific event

Typical downstream boundary conditions

constant water level time series of water level ( tidal cycle)

a reliable rating curve ( only to be used withdownstream boundaries)

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MIKE 11 IntroductionNovember 2002 Part 1

Limitations

Hydraulic jump can not be modelled

Stability conditions Sufficiently fine topographic resolution (Dx)

time step

fine enough for accurate representation of a wave at structure smaller time step is required

Courant condition to determine time step

1D

D=x

ghtCr