  We introduce novel high order well-balanced finite volume methods for the
full compressible Euler system with gravity source term. They require no a
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.

Numerical Analysis;Solar and Stellar Astrophysics;Numerical Analysis;Fluid Dynamics