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

es

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