The compressible Navier-Stokes equations converge towards their incompressible counterpart as the Mach number ε tends to zero. In the case of a weakly compressible flow, i.e. ε 〈〈 1, the resulting equations can be classified as singularly perturbed differential equations. Unfortunately, these equations set special requirements on numerical methods due to which standard discretization techniques often fail in efficiently computing an accurate approximation. One remedy is to split the equations into a stiff and a non-stiff part and then handle the stiff part implicitly and the non-stiff part explicitly in time. This procedure results in an IMEX method, with the crucial part being the choice of the splitting. In this thesis the novel RS-IMEX splitting, which uses the ε → 0 limit to split the equations by a linearization, is coupled with high order IMEX Runge-Kutta schemes. The resulting method is applied to different singularly perturbed differential equations and investigated in its behavior for ε 〈〈 1. This is done in the following steps: First, the method is applied to a class of ordinary differential equations and it is...
Rs-Imex ; Imex Runge-Kutta ; Discontinuous Galerkin ; Isentropic Euler Equations ; Low Mach ; Singularly Perturbed Differential Equations
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