= A second order well-balanced finite volume scheme for Euler equations    with gravity: general equation of state =

We present a novel well-balanced second order Godunov-type finite volume scheme for compressible Euler equations with gravity. We consider general equation of  state (EOS) for which explicit, analytical stationary solutions may not be      available. Instead we compute a discrete stationary solution using a specific   integration rule applied to the hydrostatic equations. The numerical scheme is  designed to preserve this discrete stationary solution on any mesh. When        applied to ideal gas model, the scheme exactly preserves the exact hydrostatic  solution for isothermal and polytropic cases. As an example of general EOS we   consider the ideal gas model together with radiation pressure. To study the     accuracy of the solutions in computing perturbations around the stationary      state, we solve the linearized Euler equations using a spectral collocation     method and compare the solutions from the well-balanced non-linear finite       volume scheme. These studies show that the well-balanced scheme gives accurate  predictions of perturbations around the stationary solutions. <<BR>>

'''People''': Praveen C, Jonas Berberich, Christian Klingenberg <<BR>>
'''Status''': Ongoing work