numerical activities in cosmo; physics interface; lm-z
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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 - PowerPoint PPT PresentationTRANSCRIPT
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Numerical activities in COSMO;Physics interface; LM-z
Zurich 2006
J. Steppeler (DWD)
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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
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NP=3 NP=4 NP=5
Cube 4-body Isocahedron
Rhomboidal divisions of the sphere
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Third order convergence of shallow water model at day 3
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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
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• Finite Volumes: 1
• Baumgardner Order2: 1
• Baumgardner Order3: 1
• Great circle grids: RK, SI, SL1 now 3 seem possible
• Tiled grids: 1.5
• Serendipidity grids 3
• Unstructured 1/1.3
• Conservation 1/2
Saving factors of Discretisations
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Idealized 1D advection test
analytic sol.implicit 2. orderimplicit 3. orderimplicit 4. order
C=1.580 timesteps
C=2.548 timesteps
Verbesserte Vertikaladvektion für
dynamische Var. u, v, w, T, p‘
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case study ‚25.06.2005, 00 UTC‘
total precipitation sum after 18 hwith vertical advection 2. order
difference total precpitation sum after 18 h‚vertical advection 3. order – 2. order‘
Improved vertical advektion for dynamic var. u, v, w, T, p‘
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starting point after 1 h after 1 h
modified version:pressure gradient on z-levels, if
|metric term| > |terrain follow. term|
cold pool – problem in narrow valleys
is essentially induced by pressure gradient term
T (°C)
J. Förstner, T. Reinhardt
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•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
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The step-orography
i - 1/2
i - 1/2
j - 1/2
j + 1/2
j - 1/2i + 1/2
i + 1/2j + 1/2
i, j
Shaved elements
•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
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Flow around bell shaped mountain
Atmosphere at rest
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LM_Z:
RMS of Winds and temp. against radiosondes
Frequ. Bias and threat score
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Precipitation
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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