Second Order Finite Volume Scheme for Euler Equations with Gravity which is WellBalanced for General Equations of State and Grid Systems
Abstract
We develop a second order wellbalanced finite volume scheme for compressible Euler equations with a gravitational source term. The wellbalanced 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.
 Publication:

Communications in Computational Physics
 Pub Date:
 June 2019
 DOI:
 10.4208/cicp.OA20180152
 arXiv:
 arXiv:1807.11825
 Bibcode:
 2019CCoPh..26..599B
 Keywords:

 Mathematics  Numerical Analysis;
 Physics  Computational Physics
 EPrint:
 32 pages