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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