We present a preconditioned matrix-free Newton Krylov method for solving meteorological problems with an implicit Runge-Kutta Discontinuous Galerkin scheme. First we report on an explicit version of the scheme, briefly studying serial and parallel efficiency of our code and present a comparison of our scheme with the dynamical core COSMO developed at the German Weather Service. On isotropic grids our code is shown to be competitive, while on grids with smaller spacing in the vertical than horizontal, the stability restrictions on the time step make this approach unsuitable. We then present new work on an implicit version which is shown to bring the run time back within the range of COSMO on the anisotropic grids more normally used in numerical weather prediction.
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