[hal-01098585] A Relaxation Scheme for Inviscid Flows under Gravitational Influence

Many astrophysical flows are modeled by the Euler equations with gravity source terms derived from a potential, the evolution of which is described by a Poisson equation. Several gravitational flows reach equilibrium states that are necessary to preserve in the numerical formulation. In this paper, we present the derivation of the relaxation model [17] , in which the pressure is a supplementary variable and the Poisson equation is transformed into a hyperbolic equation with a penalty parameter. The corresponding scheme is obtained in the limit as the parameter tends to zero. The proposed Riemann solver, implemented in the software HERACLES [10], provides better robustness compared to other approaches available in the same software and is capable of preserving gravitational equilibria when required. Several numerical tests and results are presented, as well.



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