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
AU - Jonas P. Berberich, Praveen Chandrashekar, Christian Klingenberg  & Friedrich K. Röpke
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 - <p style="text-align: justify;">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.</p>