Structure preserving schemes

Abstract

We present two novel structure preserving numerical schemes for the Euler equations of hydrodynamics. The first method is concerned with the exact preservation of certain hydrostatic equilibria. This is achieved by a hydrostatic preserving reconstruction procedure and a well-balanced discretization of the gravitational source term. The second method treats the deficiency of angular momentum conservation in standard Eulerian Godunov-type numerical schemes. We show the geometric requirements on a scheme that conserves mass, linear momentum, total energy and angular momentum simultaneously. We then present a scheme fulfilling these requirements. The performance of the new structure preserving schemes is illustrated through numerical examples.