%0 Generic
%A Gawlok, Simon
%C Heidelberg
%D 2017
%F heidok:23532
%K Angewandte Mathematik, Simulation, Umweltwissenschaften, Meteorologie
%R 10.11588/heidok.00023532
%T Numerical Methods for Compressible Flow with Meteorological Applications
%U https://archiv.ub.uni-heidelberg.de/volltextserver/23532/
%X In this work, the compressible Navier-Stokes equations describing the dynamics of a dry atmosphere are derived. Based on a scale analysis for Low-Mach number flows, the Low-Mach approximation is derived from the compressible Navier-Stokes equations by neglecting the hydrodynamic part of pressure, which is small compared to the hydrostatic and thermodynamic parts, in the ideal gas law. Both models are discretised by finite elements in space and finite differences in time, where all common parameters of the discretisations are chosen identically in order to minimise influences on the discrete solutions due to differences in the respective discretisation. A solution strategy for both models based on an inexact Newton method is presented, where the linear solvers and preconditioners are adapted to the respective model. In case of the Low-Mach model, a preconditioning technique based on nested Schur complement iterations is proposed. A scenario of two interacting tropical cyclones is presented as benchmark problem in order to compare the solutions of the two models in terms of numerical as well as physical properties. The obtained numerical results show the scalability and robustness of the solution approach. For the considered scenario, the predicted tracks of the cyclones, which are computed by the Low-Mach model, show very good coincidence with those of the Compressible Navier-Stokes model at significantly smaller computational costs, such that the Low-Mach approximation can be regarded as valid in this case.