Numerical comparison of Riemann solvers for astrophysical hydrodynamics
Christian Klingenberg, Wolfram Schmidt and Knut Waagan
Abstract: The idea of this work is to compare a new positive and entropy stable approximate Riemann solver by Francois Bouchut with state-of the-art algorithms for astrophysical fluid dynamics. We implemented the new Riemann solver into an astrophysical PPM-code, the Prometheus code, and also made a version with a different, more theoretically grounded higher order algorithm than PPM. We present shock tube tests, two-dimensional instability tests and forced turbulence simulations in three dimensions. We find subtle differences between the codes in the shock tube tests, and in the statistics of the turbulence simulations. The new Riemann solver increases the computational speed without significant loss of accuracy.