| Abstract: | We introduce novel high order well-balanced finite volume methods for the
full compressible Euler system with gravity source term. They require no à priori
knowledge 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 hydrostatic
state. 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, and
robust methods are not restricted to a specific equation of state. Numerical tests verify
that the proposed method improves the capability to accurately resolve small perturbations on hydrostatic states. |
