  We present a well-balanced finite volume solver for the compressible Euler
equations with gravity where the approximate Riemann solver is derived using a
relaxation approach. Besides the well-balanced property, the scheme is robust
with respect to the physical admissible states. Another feature of the method
is that it can maintain general stationary solutions of the hydrostatic
equilibrium up to machine precision. For the first order scheme we present a
well-balanced and positivity preserving second order extension using a modified
minmod slope limiter. To maintain the well-balanced property, we reconstruct in
equilibrium variables. Numerical examples are performed to demonstrate the
accuracy, well-balanced and positivity preserving property of the presented
scheme for up to 3 space dimensions.
