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, 2019)
We develop a second order well-balanced finite volume scheme for compressible Euler equations with a gravitational source term. The well-balanced propertyholds for arbitrary hydrostatic solutions of the corresponding Euler equations withoutany restriction on the equation of state. The hydrostatic solution must be known apriori either as an analytical formula or as a discrete solution at the grid points. Thescheme 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.