Limited area model weather prediction using COSMO with emphasis on the numerics of dynamical cores (including some remarks on the NEC vector supercomputer)
The current developments of the dynamical core of the COSMO model will be described. These are mainly a consolidated version of the fast waves solver in the split-explicit (horizontally explicit – vertically implicit, HE-VI) time-integration framework. The new formulation contains the use of an improved vertical discretisation. A discretisation error analysis shows the need for weighted averages in strongly stretched staggered (Lorenz) grids, in particular for the divergence operator. The use of the strong conservation form for the divergence operator potentially increases again the accuracy of metric correction terms. Further use of a Mahrer (1984) discretisation of horizontal pressure gradients allows the stable integration of steeper slopes compared to the traditional terrain following formulation. The experiences during this development with our NEC vector computer will be discussed, too.
A new test case for models using the compressible non-hydrostatic Euler equations was defined, which allows the derivation of an analytic solution. This solution is exact in the sense that it can be used for convergence studies of compressible models. The new fast waves solver is tested against this test case.
Another development branch in COSMO concerns the improvement of both the conservation properties of the dynamical core and the ability to handle steep slopes. For this purpose the usability of the anelastic Lipps, Hemler (1982) equation set and the discretisation of the EULAG model are considered. In the framework of the ‘Metström’ priority program of the German Research Community (DFG) the ‘Discontinous Galerkin’ method is inspected as another possible option of a future dynamical core for COSMO.