Second order finite volume scheme for Euler equations with gravity which is well-balanced for general equations of state and grid systems
This work provides a flexible numerical method for astrophysical and geophysical simulations where maintaining hydrostatic equilibrium is critical, though it is an incremental improvement over existing well-balanced schemes.
The authors develop a second-order well-balanced finite volume scheme for Euler equations with gravity that works for arbitrary equations of state and grid systems, maintaining the well-balanced property for any hydrostatic solution. Numerical tests confirm the scheme's accuracy and robustness.
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.