TY - JOUR T1 - A Godunov-Type Solver for the Numerical Approximation of Gravitational Flows JO - Communications in Computational Physics VL - 1 SP - 46 EP - 75 PY - 2014 DA - 2014/01 SN - 15 DO - http://doi.org/10.4208/cicp.060712.210313a UR - https://global-sci.org/intro/article_detail/cicp/7087.html KW - AB -
We present a new numerical method to approximate the solutions of an Euler-Poisson model, which is inherent to astrophysical flows where gravity plays an important role. We propose a discretization of gravity which ensures adequate coupling of the Poisson and Euler equations, paying particular attention to the gravity source term involved in the latter equations. In order to approximate this source term, its discretization is introduced into the approximate Riemann solver used for the Euler equations. A relaxation scheme is involved and its robustness is established. The method has been implemented in the software HERACLES  and several numerical experiments involving gravitational flows for astrophysics highlight the scheme.