Deutscher Wetterdienst
Working group 2:
Dynamics and Numerics
report ‘Oct. 2007 – Sept. 2008’
COSMO General Meeting, Krakau
15.-19.09.2008
Michael Baldauf
Deutscher Wetterdienst, Offenbach, Germany
FE 13 – 14.07.2017
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2.11 Alternative discretizations (due to alternative grids)
2.11.1 [RENUMBERED] Remove grid redundancy by Serendipity Grids
DWD: Steppeler
09/05 Report
The serendipity grids should be investigated, which reduce the redundancy of the
interpolation procedures. In this way they achieve more accuracy and more efficiency.
2.11.2 Higher order discretization on unstructured grids using Discontinuous Galerkin
methods
DWD: Baldauf, Univ. Freiburg: Kroener, Dedner, Brdar
2009 start, 2011 report
In the DFG priority program 'METSTRÖM' a new dynamical core for the COSMO-model will
be developed. It will use Discontinuous Galerkin methods to achieve higher order,
conservative discretizations. Currently the building of an adequate library is under
development. The work with the COSMO-model will start probably at the end of 2009. This is
therefore base research especially to clarify, if these methods can lead to efficient solvers for
NWP.
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Discontinuous Galerkin Method
• Seek weak solutions of a balance equation
(correspondance to finite volume methods  conservation)
• Expand solution into a sum of base functions on each grid cell
(correspondance to finite element methods)
•
•
•
•
DG discretization in space  arbitrary high order possible
useable on arbitrary grids  suitable for complex geometries
discontinuous elements  mass matrix is block-diagonal
in combination with an explicit time integration scheme
(e.g. Runge-Kutta  RKDG-methods)  highly parallelizable code
but: how to solve vertically expanding sound waves efficiently?
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Example of a Triangulation for 2D-flow over a mountain, produced with DUNE
(D. Kröner, A. Dedner, S. Brdar, Univ. Freiburg)
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Nonhydrostatic flow with Discontinuous Galerkin method
(polynomials of order 2), preliminary results
44 km
w [m/s]
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2.3.1 Radiative upper boundary condition
DWD: Herzog
09/05 Report
The Klemp Durran boundary is further developed.
2.3.2 [NEW] Radiative upper boundary condition; non-local in time
NN
report in 06/2009
At the University Freiburg a Radiative upper boundary condition was developed. It is
non-local in time, but nevertheless can be implemented efficiently into nonhydrostatic models. This radiation condition will be further developed during the
DFG priority program METSTROEM.
FE 13 – 14.07.2017
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New upper sponge layer (Klemp et al., 2008, MWR)
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
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Purpose: Prevent unphysical reflection of vertically propagating
gravity waves at upper model boundary
Unlike conventional damping layers, only the vertical wind is
damped; specifically this is done in the fast-wave solver
immediately after solving the tridiagonal matrix for the vertical
wind speed
Analytical calculations by Klemp et al. indicate very
homogeneous absorption properties over a wide range of
horizontal wavelengths
work by G. Zängl
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quasi-linear flow over a mountain, u = 10m/s, h = 300 m, a = 5 km, Δx = 1 km;
Fields: θ (contour interval 1 K), w (colours)
t = 24h
conventional Rayleigh damping, tdamp = 600 s
w damping, tdamp = 12 s
Depth of damping layer: 10 km; top at 22 km
FE 13 – 14.07.2017
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Deutscher Wetterdienst
quasi-linear flow over a mountain, u = 10m/s, h = 300 m, a = 5 km, Δx = 1 km;
Fields: θ (contour interval 1 K), u (colours)
t = 24h
conventional Rayleigh damping, tdamp = 600 s
w damping, tdamp = 12 s
Depth of damping layer: 10 km; top at 22 km
FE 13 – 14.07.2017
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Deutscher Wetterdienst
quasi-linear flow over a mountain, u = 10m/s, h = 300 m, a = 5 km, Δx = 1 km;
Fields: θ (contour interval 2 K), w (colours)
t = 24h
conventional Rayleigh damping, tdamp = 600 s
w damping, tdamp = 12 s
Depth of damping layer: 10 km; top at 22 km
FE 13 – 14.07.2017
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New upper sponge layer (Klemp et al., 2008, MWR)


Real-case simulations conducted so far indicate very little impact
on forecasts results
Computing costs are slightly lower because the damping is
applied to only one variable (i.e. w)
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2.6.3 Implementation of neglected diabatic terms in p'-equation
DWD: Herzog, CNMCA: L. Torrisi
Talk by L. Torrisi
2.10 Diagnostic tools
2.10.1 Application of the integration tool to energy, mass balance
DWD: Baldauf, MPI-H: Petrik
The integration tool to calculate balance equations by volume integrations of densities
and surface integrations of fluxes developed in the Priority project 'Runge-Kutta', Task
3 will be applied to questions of energy and mass budgets.
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Parallel session
New priority project CDC
at 16:30 in Room E
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