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**Modelling tools - MIKE11 Part1-Introduction**

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**‘A model is a caricature of reality.´ R. May **

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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**Understand the problem**

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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**Mike 11 includes the following modules**

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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**Open channel flow- Saint Venant equations (1D)**

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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**Momentum conservation**

Equations Mass conservation Momentum conservation

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**Independent variables**

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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**Depending on how many terms are used in momentum equations**

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 Full Saint Venant equations are used when there is a rapid change in the water depth over time, and water discharge is significantly higher than the available calibration data When differences in space are to be computed, the question is if the values in time step j or time step j+1 should be used. If the time step j is used an explicit solution is given. If the values at time j+1 are used, an implicit solution is given. An implicit solution is more stable than an explicit one and longer time step can be used. An explicit solution is simpler to program.

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**Neglect first two terms**

Flow description Neglect first two terms Diffusive wave ( backwater analysis) Neglect three terms 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 h1 h3 h5 h7 2 4 6 Q Center point

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**Boundary conditions Initial condition Solution scheme**

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 R h

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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

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**User-defined culverts Q-h calculated culverts Dam break structure**

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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**View results - Mike view Print results - Mike print **

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 !!

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Mathematical Background

Mathematical Background

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