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A Relaxation Scheme for Inviscid Flows under Gravitational Influence

Abstract : 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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Submitted on : Wednesday, January 14, 2015 - 7:02:53 PM
Last modification on : Tuesday, September 28, 2021 - 2:10:07 PM

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Jeaniffer Vides, Edouard Audit, Boniface Nkonga. A Relaxation Scheme for Inviscid Flows under Gravitational Influence. Congrès SMAI 2013, Sep 2014, Seignosse le Penon, France. pp.523-532, ⟨10.1051/proc/201445054⟩. ⟨hal-01103515⟩