A Godunov-Type Solver for the Numerical Approximation of Gravitational Flows (Communications in Computational Physics, 2014)
We present a new numerical method to approximate the solutions of anEuler-Poisson model, which is inherent to astrophysical flows where gravity plays animportant role. We propose a discretization of gravity which ensures adequate coupling of the Poisson and Euler equations, paying particular attention to the gravitysource 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. Themethod has been implemented in the software HERACLES [29] and several numericalexperiments involving gravitational flows for astrophysics highlight the scheme.