  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 a large class of 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. The
resulting scheme is very simple and can be implemented into any existing finite
volume code with minimal effort. Moreover, the scheme is not tied to any
particular form of the equation of state, which is crucial for example in
astrophysical applications. Several numerical experiments demonstrate the
robustness and high-order accuracy of the scheme nearby and out of hydrostatic
equilibrium.
