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A Godunov-type solver for the numerical approximation of gravitational flows. (English) Zbl 1373.85005

Summary: 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 [29] and several numerical experiments involving gravitational flows for astrophysics highlight the scheme.

MSC:

85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
85-08 Computational methods for problems pertaining to astronomy and astrophysics
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
76E20 Stability and instability of geophysical and astrophysical flows

Software:

HERACLES
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