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Implicit Time Stepping for Orographic Flow: A Cloud Resolving Model Approach

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This paper presents a cloud-resolving model with implicit time stepping, developed by Oswald Knoth and Detlev Hinneburg at the Institute for Tropospheric Research, Leipzig, Germany. The model is based on an anelastic framework, incorporating momentum equations, potential temperature, continuity equations, and water vapor dynamics. Utilizing a cut-cell approach, it allows for accurate representation of orographic cloud formation and dynamics under varying conditions. The model is validated through simulations of an orographic cloud hill and moist bubble scenarios, demonstrating its robustness and efficiency in handling complex atmospheric processes.

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Implicit Time Stepping for Orographic Flow: A Cloud Resolving Model Approach

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  1. A cloud resolving model with implicit time stepping: orographic flow application Oswald Knoth, Detlev Hinneburg Institute for Tropospheric Research, Leipzig, Germany

  2. Model Formulation anelastic model Momentum equation Potential temperature Continuity equation Water vapour Cloud water Bad Orb 2003

  3. Source terms Bad Orb 2003

  4. Buoyancy Bad Orb 2003

  5. Condensation/Evaporation Bad Orb 2003

  6. Condensation/Evaporation Bad Orb 2003

  7. Condensation/Evaporation Bad Orb 2003

  8. Cut Cell Approach Grid is described by free face area F Free cell Volume V Bad Orb 2003

  9. Free face aerea Free volume Cut Cell Approach Bad Orb 2003

  10. step size approximation at time approximation of the Jacobian Time integration method by a projected Rosenbrock method Bad Orb 2003

  11. Including of Projection Bad Orb 2003

  12. Jacobian: Transport: Advection Diffusion Source: Bouyancy Condensation Drag Curvature effects Coriolis force Solution of the linear systems a)Rosenbrock step CG-method (BiCGStab) with preconditioning Bad Orb 2003

  13. replaced by first order upwinding is inverted approximately by Gauss-Seidel iteration, is inverted exactly Solution of the linear systems Preconditioner: approximate matrix factorization Reduction of matrix operations through Bad Orb 2003

  14. Solution of the linear systems b) Pressure solver Nonoverlapping domain decomposition Inner variables: cell centered pressure Interface variables: pressure gradient Global problem indefinit: preconditioned QMR Preconditioner: Neumann and Dirichlet problems on each subdomain (Multigrid) Coarse problem: Neumann like problem with one variable for each subdomain Bad Orb 2003

  15. Example: Orographic Cloud Hill is described by Witch of Agnessi mountain, defined by A stable atmosphere is used with 90% relative humidity Bad Orb 2003

  16. Orographic Cloud Bad Orb 2003

  17. Orographic Cloud Bad Orb 2003

  18. Orographic Cloud 0 sec. Bad Orb 2003

  19. Orographic Cloud 0 sec. Bad Orb 2003

  20. Orographic Cloud 1000 sec. Bad Orb 2003

  21. Orographic Cloud 1500 sec. Bad Orb 2003

  22. Orographic Cloud 2000 sec. Bad Orb 2003

  23. Orographic Cloud 3000 sec. Bad Orb 2003

  24. Orographic Cloud 3000 sec. Bad Orb 2003

  25. Orographic Cloud 3000 sec. Bad Orb 2003

  26. Orographic Cloud Bad Orb 2003

  27. Moist Bubble Computational domain 3,6 km by 2,4 km, dx=dz=10 m Bad Orb 2003

  28. Moist Bubble 0 min. Bad Orb 2003

  29. Moist Bubble 4 min. Bad Orb 2003

  30. Moist Bubble 6 min. Bad Orb 2003

  31. Moist Bubble 8 min. Bad Orb 2003

  32. Moist Bubble 8 min. Bad Orb 2003

  33. Moist Bubble 8 min. Bad Orb 2003

  34. Moist Bubble Bad Orb 2003

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