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Numerical activities in COSMO; Physics interface; LM-z

Numerical activities in COSMO; Physics interface; LM-z. Zurich 2006 J. Steppeler (DWD). Is there a vision towards 2010?. Energy and Mass conservation Approximation order 3 avoiding violation of approximation conditions: Rational physics interface

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Numerical activities in COSMO; Physics interface; LM-z

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  1. Numerical activities in COSMO;Physics interface; LM-z Zurich 2006 J. Steppeler (DWD)

  2. Is there a vision towards 2010? Energy and Mass conservation Approximation order 3 avoiding violation of approximation conditions: Rational physics interface Terrain intersecting grid (cut cell method) Serendipidity grids Grids on the sphere

  3. Rhomboidal divisions of the sphere NP=3 NP=4 NP=5 Cube 4-body Isocahedron

  4. Third order convergence of shallow water model at day 3

  5. Numerical activities in COSMO Semi-Implicit method on distributed memory computers using Green functions Two main projects LM_RK: Runge Kutta time integration, Order 3 LM_Z: Cut cell terrain intersecting discretisation

  6. Saving factors of Discretisations • Finite Volumes: 1 • Baumgardner Order2: 1 • Baumgardner Order3: 1 • Great circle grids: RK, SI, SL 1 now 3 seem possible • Tiled grids: 1.5 • Serendipidity grids 3 • Unstructured 1/1.3 • Conservation 1/2

  7. Verbesserte Vertikaladvektion für dynamische Var. u, v, w, T, p‘ analytic sol. implicit 2. order implicit 3. order implicit 4. order C=1.5 80 timesteps Idealized 1D advection test C=2.5 48 timesteps

  8. case study ‚25.06.2005, 00 UTC‘ Improved vertical advektion for dynamic var. u, v, w, T, p‘ total precipitation sum after 18 h with vertical advection 2. order difference total precpitation sum after 18 h ‚vertical advection 3. order – 2. order‘

  9. cold pool – problem in narrow valleys is essentially induced by pressure gradient term T (°C) starting point after 1 h after 1 h modified version: pressure gradient on z-levels, if |metric term| > |terrain follow. term| J. Förstner, T. Reinhardt

  10. Coordinates cut into mountains • The finite volume cut cell is used for discretisation / unstructured grid • Boundary structures are kept over mountains (vertically unstructured • The violation of an approximation error is avoided LM_Z

  11. i + 1/2 i - 1/2 j + 1/2 j + 1/2 i, j j - 1/2 j - 1/2 i - 1/2 i + 1/2 Shaved elements The step-orography • The shaved elements are mathematically more correct than step boundaries • By shaved elements the z-coordinate is improved such that the criticism of Gallus and Klemp (2000), Mon. Wea. Rev. 128, 1153-1164 no longer applies • New results: MWR, in print

  12. Flow around bell shaped mountain Atmosphere at rest

  13. Frequ. Bias and threat score LM_Z: RMS of Winds and temp. against radiosondes

  14. Precipitation

  15. Conclusions • Existing physics interfaces and terrain following grids violate approximation conditions • LM_RK: High order approximation • LM_Z: Terrain intersecting method taken over from CFD • Better flow over obstacles • Better vertical velocities and precipitation

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