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Introduction to MIKE 11 by Bunchingiv Bazartseren

Introduction to MIKE 11 by Bunchingiv Bazartseren. Cottbus May 22, 2001. Outline. General Hydrodynamics within MIKE 11 flow types numerical solution Modelling with MIKE 11 Example demonstration input preparation simulation visualization. General 1. 1D flow (wave) simulation

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Introduction to MIKE 11 by Bunchingiv Bazartseren

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

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

  3. General1 • 1D flow (wave) simulation • Application into water system • for what purpose? • design • management • operation • where? • river • estuaries • irrigation systems Introduction to MIKE 11

  4. General2 • 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 Introduction to MIKE 11

  5. ¶ Q A + = q ¶ ¶ x t æ ö 2 Q ç ÷ ¶ a ç ÷ ¶ ¶ gQ Q A Q h è ø + + + = gA 0 ¶ ¶ ¶ 2 t x x C AR Saint Venant equation1 • Unsteady, nearly horizontal flow • 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-1 • R - hydraulic radius, m • a -momentum distribution coefficient Introduction to MIKE 11

  6. Saint Venant equation2 • 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) Introduction to MIKE 11

  7. Diffusive wave - no inertia ¶ Q Q h - + = gA gAi g 0 ¶ 2 x C RA • Kinematic wave - pure convective ¶ h - = i 0 ¶ x Flow types • Fully dynamic Introduction to MIKE 11

  8. + ¶ - n 1 n x x x @ ¶ D t t Finite difference method • Discretization into time and space • Difference between explicit and implicit scheme Introduction to MIKE 11

  9. ( ) ( ) + + + + n 1 n n 1 n Q Q Q Q + + - - j 1 j 1 j 1 j 1 - ¶ Q 2 2 = ¶ D x 2 x j Solution scheme1 • Structured, cartesian grid • Implicit scheme (Abbott-Ionescu) • Continuity equation - h centered • Momentum equation - Q centered Example discretization: Introduction to MIKE 11

  10. + + + + + = 1 1 1 n n n A 1 Q B 1 h C 1 Q D 1 - - 1 1 j j j j j j j + + + + + = 1 1 1 n n n A 1 h B1 Q C 1 h D 1 - - 1 1 j j j j j j j + + + f + f + f = n 1 n 1 n 1 A 1 B 1 C 1 D 1 - - j j 1 j j j j 1 j 0 1 2 . . jj D0 D1 D2 . . Djj • Tri-diagonal matrix form of equation n+1 n A0 B0C0 A1B1 C1 A2B2 C2 . . . . . . AjjBjj Cjj all zeros . = all zeros Solution scheme2 • Transformation into linear equations (mass) (momentum) Introduction to MIKE 11

  11. + + f = f + n 1 n 1 E F + j 1 j j j • Substitution of into the linear equations • Derivation of recurrence relations - C j = E - 1 j + A E B j j j - D A C j j j = F - 1 j + A E B j j j Solution scheme3 • Less equation than unknowns • Use of suitable boundary conditions • Introducing additional variables Introduction to MIKE 11

  12. Solution scheme4 • Double sweep algorithm • calculate the coefficients A-D • obtain Ejj, Fjj from right hand boundary • sweep forward to calculate Ej, Fj • sweep back to calculate jn+1 for all grid Introduction to MIKE 11

  13. Network of open channels1 • Use of graph theory • Set of vertices and edges • edges - channels • nodes - river confluence Introduction to MIKE 11

  14. edges  1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 nodes Network of open channels2 • Incidence matrix from the network • Confluence nodes - h boundary • Each channel - diagonal matrix • Consideration of lateral flow Introduction to MIKE 11

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