High-order well-balanced finite volume schemes for the Euler equations with gravitation

A high-order well-balanced scheme for the Euler equations with gravitation is presented. The scheme is able to preserve a spatially high-order accurate discrete representation of isentropic hydrostatic equilibria. It is based on a novel local hydrostatic reconstruction, which, in combination with any standard high-order accurate reconstruction procedure, achieves genuine high-order accuracy for smooth solutions close or away from equilibrium....