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
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3. Source terms
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4. Buoyancy
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5. Condensation/Evaporation
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6. Condensation/Evaporation
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7. Condensation/Evaporation
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8. Cut Cell Approach Grid is described by free face area F
Free cell Volume V
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9. Cut Cell Approach
Free face aerea
Free volume
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10. Time integration method by a projected Rosenbrock method
approximation at time
step size
approximation of the Jacobian
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11. Including of Projection
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12. Solution of the linear systems
a)Rosenbrock step
CG-method (BiCGStab) with preconditioning
Jacobian:
Transport: Advection
Diffusion
Source: Bouyancy
Condensation
Drag
Curvature effects
Coriolis force
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13. Solution of the linear systems
replaced by first order upwinding
Preconditioner: approximate matrix factorization
is inverted approximately by Gauss-Seidel iteration,
is inverted exactly
Reduction of matrix operations through
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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
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15. Example: Orographic Cloud
Hill is described by Witch of Agnessi mountain, defined by
A stable atmosphere is used with 90% relative humidity
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16. Orographic Cloud
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17. Orographic Cloud
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18. Orographic Cloud
0 sec.
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19. Orographic Cloud
0 sec.
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20. Orographic Cloud
1000 sec.
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21. Orographic Cloud
1500 sec.
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22. Orographic Cloud
2000 sec.
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23. Orographic Cloud
3000 sec.
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24. Orographic Cloud
3000 sec.
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25. Orographic Cloud
3000 sec.
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26. Orographic Cloud
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27. Moist Bubble Computational domain 3,6 km by 2,4 km, dx=dz=10 m
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28. Moist Bubble
0 min.
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29. Moist Bubble
4 min.
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30. Moist Bubble
6 min.
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31. Moist Bubble
8 min.
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32. Moist Bubble
8 min.
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33. Moist Bubble
8 min.
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34. Moist Bubble
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