1. MIKE 11 IntroductionNovember 2002Part 1 Introduction to MIKE 11 Part 1 General Hydrodynamics within MIKE 11 –Basic Equations –Flow Types Numerical Scheme

2. MIKE 11 IntroductionNovember 2002Part 1 General Simulation of 1D Flow in –Estuaries, –Rivers and –Irrigation Systems, etc. Application for Inland Water System –Design, –Management and –Operation

3. MIKE 11 IntroductionNovember 2002Part 1 Main Modules Rainfall-Runoff Hydrodynamics Advection-Dispersion and Cohesive Sediment Water Quality Non Cohesive Sediment Transport

4. MIKE 11 IntroductionNovember 2002Part 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

5. MIKE 11 IntroductionNovember 2002Part 1 de Saint Venant Equations (Mass and Momentum Conservation): 0 q 2 2                        ARC QgQ x h gA x A Q t Q t A x Q  where, Q - discharge, m 3 s -1 A - flow area, m 2 q - lateral flow, m 2 s -1 h - depth above datum, m C - Chezy resistance coefficient, m 1/2 s -1 R - hydraulic radius, m  - momentum distribution coefficient

6. MIKE 11 IntroductionNovember 2002Part 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

7. MIKE 11 IntroductionNovember 2002Part 1 Flow Types –Neglect first two terms Diffusive wave ( backwater analysis)

8. MIKE 11 IntroductionNovember 2002Part 1 Flow Types –Neglect three terms Kinematic wave (relatively steep rivers without backwater effects)

9. MIKE 11 IntroductionNovember 2002Part 1 Finite Difference Method Discretisation in time and space t xx t x nn       1

10. MIKE 11 IntroductionNovember 2002Part 1 Numerical 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

11. MIKE 11 IntroductionNovember 2002Part 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             Implicit Finite Difference Scheme (Abbott- Ionescu) Continuity equation - h centered Momentum equation - Q centered

12. MIKE 11 IntroductionNovember 2002Part 1 Boundary Conditions 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

13. MIKE 11 IntroductionNovember 2002Part 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 with downstream boundaries)

14. MIKE 11 IntroductionNovember 2002Part 1 Limitations Hydraulic jump can not be modelled Stability conditions –Sufficiently fine topographic resolution (  x) – time step fine enough for accurate representation of a wave at structure smaller time step is required Courant condition to determine time step