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Mathematics > Numerical Analysis

arXiv:1807.11825 (math)
[Submitted on 31 Jul 2018 (v1), last revised 2 Aug 2018 (this version, v2)]

Title:Second order finite volume scheme for Euler equations with gravity which is well-balanced for general equations of state and grid systems

Authors:Jonas P. Berberich, Praveen Chandrashekar, Christian Klingenberg, Friedrich K. Röpke
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Abstract:We develop a second order well-balanced finite volume scheme for compressible Euler equations with a gravitational source term. The well-balanced property holds for arbitrary hydrostatic solutions of the corresponding Euler equations without any restriction on the equation of state. The hydrostatic solution must be known a priori either as an analytical formula or as a discrete solution at the grid points. The scheme can be applied on curvilinear meshes and in combination with any consistent numerical flux function and time stepping routines. These properties are demonstrated on a range of numerical tests.
Comments: 32 pages
Subjects: Numerical Analysis (math.NA); Computational Physics (physics.comp-ph)
Cite as: arXiv:1807.11825 [math.NA]
  (or arXiv:1807.11825v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1807.11825
Related DOI: https://doi.org/10.4208/cicp.OA-2018-0152

Submission history

From: Jonas Berberich [view email]
[v1] Tue, 31 Jul 2018 14:05:17 UTC (5,502 KB)
[v2] Thu, 2 Aug 2018 08:02:59 UTC (5,502 KB)
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