Download - Mike11 Equations
IHE 2002-2003
Modelling tools - MIKE11Part1-Introduction
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What is a model ?
• ‘A model is a caricature of reality.´
R. May • A model is a simplification of reality that retains
enough aspects of the original system to make it useful to the modeler
• Models may take many forms– phisical models ( hydrologic models of watersheds; scales
models of ships)
– conceptual (differential equations, optimization)
– simulation models
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The modelling process
• Understand the problem– reason to model a system ( e.g. what if a dam is built?)– collect and analyse data
• Choosing variables• Set up mathematical model
– describe situation– write mathematical explanation using variables
• Assumptions about the system• Construction of the mathematical model• Computer simulation
– computer program– input data and runs– validation
• Simulation experiments– interpret the solution, test outcomes– improve the model
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Classification of modelling packages
• According to what is computed– water surface profiles (HEC2)
– flood waves (DAMBRK)
– water quality in rivers (QUAL2E)
– habitat modelling (PHABSIM)
• How many dimensions are used– 1D models (MIKE11, SOBEK)
– 2D models
– 3D models (DELFT3D)
• Particulars of the numerical methods– finite differences
– finite elements
– boundary elements
– etc
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MIKE11 - General description
• Software package developed by Danish Hydraulic Institute (DHI) for simulation of flow, sediment transport and water quality in estuaries, river, irrigation system and similar water bodies
• User - friendly tool for design, management and operation of river basins and channel networks
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Implementation
• Mike 11 includes the following modules– HD - hydrodynamic - simulation of unsteady flow in a
network of open channels. Result is time series of discharges and water levels;
– AD - advection dispersion
– WQ - water quality
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Theory
• Open channel flow- Saint Venant equations (1D)– continuity equation (mass conservation)
– momentum equation (fluid momentum conservation)
• Assumptions– water is incompresible and homogeneous
– bottom slope is small
– flow everywhere is paralel to the bottom ( i.e. wave lengths are large compared with water depths)
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Hydraulic variables
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Equations
• Mass conservation
qt
A
x
Q
• Momentum conservation
0
2
2
ARC
QgQ
x
hgA
x
AQ
t
Q
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Equations 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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Flow description
• Depending on how many terms are used in momentum equations– full Saint Venant equations (dynamic wave)
• explicit methods
• implicit methods
Time step j+1
Time step j
Time step j-1
Cross section i Cross section i+1 Cross section i-1
Space
Time
Reach
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Flow description
– Neglect first two terms
0
2
2
ARC
QgQ
x
hgA
x
AQ
t
Q
• Diffusive wave ( backwater analysis)
– Neglect three terms
0
2
2
ARC
QgQ
x
hgA
x
AQ
t
Q
• Kinematic wave (relatively steep rivers without backwater effects)
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Solution scheme
• Equations are transformed to a set of implicit finite difference equations over a computational grid– alternating Q - and H points, where Q and H are computed at each time
step
– numerical scheme - 6 point Abbott-Ionescu scheme
Time step n+1/2
Time step n
Time Time step n+1
i i+1 i-1
Space
h1h3
h5
h7
2
4
6
Q
Q
Q
Center point
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Solution scheme
• Boundary conditions– external boundary conditions - upstream and downstream;
– internal “boundary conditions” - hydraulic structures ( here Saint Venant equation are not applicable)
• Initial condition – time t=0
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Choice of 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 with downstream boundaries)
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Discretization - branches
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Discretization - branches
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Discretization - cross sections
• Required at representative locations throughout the branches of the river
• Must accurately represent the flow changes, bed slope, shape, flow resistance characteristics
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Discretization - cross section
• Friction formulas– Chezy
– Manning
• For each section a curve is made with wetted area, conveyance factor, hydraulic radius as a function of water level
h
R
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Avoiding Errors
• Hydraulic jump can not be modelled, but upstream and downstream condition can
• Stability conditions– topographic resolution must be sufficiently fine (x)
– time step • should be fine enough to provide accurate representation of a wave
• if structure are used smaller time step is required
• use Courant condition to determine time step
• or velocity condition
x
ghvtCr
2 to1x
tv
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Structures
• Broadcrested weirs• Special weirs• User-defined culverts• Q-h calculated culverts• Dam break structure
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Mike 11 main menu
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Used files
• For Simulation– network file *.mwk11
– cross section *.xns11
– boundary *.bnd11
– time series file *.dfs0
– hd parameters *.hd11
– simulation *.sim11
– result file *.res
• View results - Mike view• Print results - Mike print• Demos - Cali and Vida rivers
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Assignement
• Solve task 1, 2 and 3 using MIKE11. Task 1 you have to built the simulation files and to run the simulation. For task 2 and 3 you must examine the prepared data files, perform a calculation and check the results. If results are not good, identify the cause and correct the situation.
• Exercises from task 2 and 3 should be submitted before week 49 or on Monday , December 3-rd
Good luck !!