| Summary: | 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
? , 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 ? , 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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