1. Introduction to MIKE 11 by Bunchingiv Bazartseren Cottbus May 22, 2001

2. May 22, 2001Introduction to MIKE 11 Outline General Hydrodynamics within MIKE 11 flow types numerical solution Modelling with MIKE 11 Example demonstration input preparation simulation visualization

3. May 22, 2001Introduction to MIKE 11 General 1 1D flow (wave) simulation Application into water system for what purpose? design management operation where? river estuaries irrigation systems

4. May 22, 2001Introduction to MIKE 11 General 2 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

5. May 22, 2001Introduction to MIKE 11 Saint Venant equation 1 Unsteady, nearly horizontal flow 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. May 22, 2001Introduction to MIKE 11 Saint Venant equation 2 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)

7. May 22, 2001Introduction to MIKE 11 Flow types Fully dynamic 0 2    RAC QQ ggAi x h gA Diffusive wave - no inertia Kinematic wave - pure convective 0    i x h

8. May 22, 2001Introduction to MIKE 11 Finite difference method Discretization into time and space t xx t x nn       1 Difference between explicit and implicit scheme

9. May 22, 2001Introduction to MIKE 11 Solution scheme 1 Structured, cartesian grid Implicit scheme (Abbott-Ionescu) Continuity equation - h centered Momentum equation - Q centered  j n j n j n j n j x QQQQ x Q 2 22 1 1 11 1 1             Example discretization:

10. May 22, 2001Introduction to MIKE 11 Transformation into linear equations Solution scheme 2 j n jj n jj n jj j n jj n jj n jj DhCQB1B1hA DQChBQA 111 1111 1 1 11 1 1 1 11 1           j n jj n jj n jj DCBA1111 1 1 11 1       Tri-diagonal matrix form of equation A 0 B 0 C 0 A 1 B 1 C 1 A 2 B 2 C 2... A jj B jj C jj  0  1  2.  jj D 0 D 1 D 2. D jj n+1n =. all zeros (mass) (momentum)

11. May 22, 2001Introduction to MIKE 11 Less equation than unknowns Use of suitable boundary conditions Introducing additional variables Solution scheme 3 Substitution of into the linear equations Derivation of recurrence relations jjj jjj j jjj j j BEA CAD F BEA C E         1 1 j n jj n j FE    11 1 

12. May 22, 2001Introduction to MIKE 11 Double sweep algorithm calculate the coefficients A-D obtain E jj, F jj from right hand boundary sweep forward to calculate E j, F j sweep back to calculate  j n+1 for all grid Solution scheme 4

13. May 22, 2001Introduction to MIKE 11 Network of open channels 1 Use of graph theory Set of vertices and edges edges - channels nodes - river confluence

14. May 22, 2001Introduction to MIKE 11 Incidence matrix from the network Confluence nodes - h boundary Each channel - diagonal matrix Consideration of lateral flow Network of open channels 2 1 1 1 1 1 1 1 1 1 edges nodes 113131113131 