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
•Terrain intersecting grid (cut cell method)
•Serendipidity grids
•Grids on the sphere
Rhomboidal divisions of the
sphere
NP=3
NP=4
NP=5
Cube
4-body
Isocahedron
Third order convergence of shallow
water model at day 3
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
Saving factors of Discretisations
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Finite Volumes:
Baumgardner Order2:
Baumgardner Order3:
Great circle grids: RK, SI, SL
Tiled grids:
1.5
Serendipidity grids
Unstructured
Conservation
1
1
1
1 now
3
1/1.3
1/2
3 seem possible
analytic sol.
implicit 2. order
implicit 3. order
implicit 4. order
C=1.5
80 timesteps
Verbesserte
Vertikaladvektion
für
dynamische Var. u, v,
w, T, p‘
Idealized 1D advection test
C=2.5
48 timesteps
case study
‚25.06.2005, 00 UTC‘
total precipitation sum after 18 h
with vertical advection 2. order
Improved vertical
advektion for
dynamic var. u, v,
w, T, p‘
difference total precpitation sum after 18 h
‚vertical advection 3. order – 2. order‘
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
LM_Z
•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
The step-orography
Shaved elements
•The shaved elements are
mathematically more correct than
step boundaries
•By shaved elements the zcoordinate is improved such that the
criticism of Gallus and Klemp
(2000), Mon. Wea. Rev. 128, 11531164 no longer applies
•New results: MWR, in print
j + 1/2
i + 1/2
j + 1/2
i - 1/2
i, j
j - 1/2
i - 1/2
j - 1/2
i + 1/2
Flow around bell
shaped mountain
Atmosphere at rest
Frequ. Bias and threat
score
LM_Z:
RMS of Winds and temp. against
radiosondes
Precipitation
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