High Order Discretely Well-Balanced Methods for Arbitrary Hydrostatic Atmospheres (Communications in Computational Physics, 2021)
We introduce novel high order well-balanced finite volume methods for thefull compressible Euler system with gravity source term. They require no à prioriknowledge of the hydrostatic solution which is to be well-balanced and are not restricted to certain classes of hydrostatic solutions. In one spatial dimension we construct a method that exactly balances a high order discretization of any hydrostaticstate. The method is extended to two spatial dimensions using a local high order approximation of a hydrostatic state in each cell. The proposed simple, flexible, androbust methods are not restricted to a specific equation of state. Numerical tests verifythat the proposed method improves the capability to accurately resolve small perturbations on hydrostatic states.