Introduction to MIKE 11 by Bunchingiv Bazartseren
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Transcript of Introduction to MIKE 11 by Bunchingiv Bazartseren
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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