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Volume 26, Issue 2
Second Order Finite Volume Scheme for Euler Equations with Gravity which is Well-Balanced for General Equations of State and Grid Systems

Jonas P. Berberich, Praveen Chandrashekar, Christian Klingenberg & Friedrich K. Röpke

DOI: 10.4208/cicp.OA-2018-0152

Commun. Comput. Phys., 26 (2019), pp. 599-630.

Published online: 2019-04

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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 to 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.

  • Keywords

Finite volume methods, well-balancing, compressible Euler equations with gravity.

  • AMS Subject Headings

76M12, 65M08, 65M20, 35L65, 76N15, 76E20, 85-08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-26-599, author = {}, title = {Second Order Finite Volume Scheme for Euler Equations with Gravity which is Well-Balanced for General Equations of State and Grid Systems}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {2}, pages = {599--630}, 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 to 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0152}, url = {http://global-sci.org/intro/article_detail/cicp/13104.html} }
TY - JOUR T1 - Second Order Finite Volume Scheme for Euler Equations with Gravity which is Well-Balanced for General Equations of State and Grid Systems JO - Communications in Computational Physics VL - 2 SP - 599 EP - 630 PY - 2019 DA - 2019/04 SN - 26 DO - http://doi.org/10.4208/cicp.OA-2018-0152 UR - https://global-sci.org/intro/article_detail/cicp/13104.html KW - Finite volume methods, well-balancing, compressible Euler equations with gravity. AB -

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 to 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.

Jonas P. Berberich, Praveen Chandrashekar, Christian Klingenberg & Friedrich K. Röpke. (2019). Second Order Finite Volume Scheme for Euler Equations with Gravity which is Well-Balanced for General Equations of State and Grid Systems. Communications in Computational Physics. 26 (2). 599-630. doi:10.4208/cicp.OA-2018-0152
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