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arXiv · 1612.03910

A numerical scheme for the compressible low-Mach number regime of ideal fluid dynamics

Wasilij Barsukow·Philipp V. F. Edelmann·Christian Klingenberg·Fabian Miczek·Friedrich K. Roepke
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Abstract

Based on the Roe solver a new technique that allows to correctly represent low Mach number flows with a discretization of the compressible Euler equations was proposed in Miczek et al.: New numerical solver for flows at various mach numbers. A&A 576, A50 (2015). We analyze properties of this scheme and demonstrate that its limit yields a discretization of the continuous limit system. Furthermore we perform a linear stability analysis for the case of explicit time integration and study the performance of the scheme under implicit time integration via the evolution of its condition number. A numerical implementation demonstrates the capabilities of the scheme on the example of the Gresho vortex which can be accurately followed down to Mach numbers of ~1e-10 .

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Wasilij Barsukow, Philipp V. F. Edelmann, Christian Klingenberg, Fabian Miczek, Friedrich K. Roepke. 2016-12-12. A numerical scheme for the compressible low-Mach number regime of ideal fluid dynamics. https://arxiv.org/abs/1612.03910

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