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Michael Baldauf Deutscher Wetterdienst, Offenbach, Germany

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. 2.11 Alternative discretizations (due to alternative grids)

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Michael Baldauf Deutscher Wetterdienst, Offenbach, Germany

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  1. Working group 2:Dynamics and Numerics report ‘Oct. 2007 – Sept. 2008’COSMO General Meeting, Krakau15.-19.09.2008 Michael Baldauf Deutscher Wetterdienst, Offenbach, Germany

  2. 2.11 Alternative discretizations (due to alternative grids) 2.11.1  [RENUMBERED] Remove grid redundancy by Serendipity GridsDWD: 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.

  3. DiscontinuousGalerkinMethod • Seekweaksolutionsof a balanceequation(correspondanceto finite volumemethods conservation) • Expandsolutioninto a sumofbasefunctions on eachgridcell(correspondanceto finite elementmethods) • DGdiscretization in space arbitraryhigh order possible • useable on arbitrarygrids  suitableforcomplex geometries • discontinuouselements  massmatrixis block-diagonal • in combinationwith an explicit time integrationscheme(e.g. Runge-Kutta  RKDG-methods)  highlyparallelizablecode • but: howtosolveverticallyexpandingsoundwavesefficiently?

  4. Example of a Triangulation for 2D-flow over a mountain, produced with DUNE(D. Kröner, A. Dedner, S. Brdar, Univ. Freiburg)

  5. Nonhydrostatic flow with Discontinuous Galerkin method(polynomials of order 2), preliminary results 44 km w [m/s]

  6. 2.3.1   Radiative upper boundarycondition 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 non-hydrostatic models. This radiation condition will be further developed during the DFG priority program METSTROEM.

  7. New upper sponge layer (Klemp et al., 2008, MWR) • 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

  8. 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

  9. 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

  10. 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

  11. 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)

  12. 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.

  13. Parallel session New priority project CDC at 16:30 in Room E

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