1. Deutscher Wetterdienst 1FE 13 – 10.03.2016 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. Deutscher Wetterdienst 2FE 13 – 10.03.2016 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.

3. Deutscher Wetterdienst 3FE 13 – 10.03.2016 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?

4. Deutscher Wetterdienst 4FE 13 – 10.03.2016 Example of a Triangulation for 2D-flow over a mountain, produced with DUNE (D. Kröner, A. Dedner, S. Brdar, Univ. Freiburg)

5. Deutscher Wetterdienst 5FE 13 – 10.03.2016 Nonhydrostatic flow with Discontinuous Galerkin method (polynomials of order 2), preliminary results 44 km w [m/s]

6. Deutscher Wetterdienst 6FE 13 – 10.03.2016 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 non- hydrostatic models. This radiation condition will be further developed during the DFG priority program METSTROEM.

7. Deutscher Wetterdienst 7FE 13 – 10.03.2016 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. Deutscher Wetterdienst 8FE 13 – 10.03.2016 conventional Rayleigh damping, t damp = 600 sw damping, t damp = 12 s 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 Depth of damping layer: 10 km; top at 22 km

9. Deutscher Wetterdienst 9FE 13 – 10.03.2016 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, t damp = 600 sw damping, t damp = 12 s Depth of damping layer: 10 km; top at 22 km

10. Deutscher Wetterdienst 10FE 13 – 10.03.2016 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, t damp = 600 sw damping, t damp = 12 s Depth of damping layer: 10 km; top at 22 km

11. Deutscher Wetterdienst 11FE 13 – 10.03.2016 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. Deutscher Wetterdienst 12FE 13 – 10.03.2016 2.6.3 Implementation of neglected diabatic terms in p'-equation DWD: Herzog, CNMCA: 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. Talk by L. Torrisi

13. Deutscher Wetterdienst 13FE 13 – 10.03.2016 Parallel session New priority project CDC at 16:30 in Room E