Modellierung und Approximation feuchter atmosphärischer Strömungen unter Berücksichtigung topographischer Effekte

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In fluid dynamics conservation properties attract a great deal of attention. In the presence of moist processes phase boundaries can be modelled by discontinuities. Therefore a mathematically appropriate formulation are the conservation laws for mass, momentum and energy in weak form. In meteorological modelling there exist numerous alternative formulations which allow for simple discretisations taking care of discontinuities in one way or another. In this project we compare mass- and momentum conserving methods which differ in their description of thermodynamic processes. We consider and compare two different classes of finite volume methods: wave-propagation methods (where the numerical flux is based on the solution of local Riemann problems) and methods which are traditionally used in numerical weather prediction (NWP) (where in each component the flux is obtained by interpolation). To address meteorological problems with some prospect of success numerical methods should be able to cope with orography, small Mach- and Froude numbers, as well as with stiff phase transition processes. We use discretisations on Cartesian grids including cut cells at embedded boundaries.