A Godunov-Type Solver for Gravitational Flows: Towards a Time-Implicit Version in the HERACLES Code

Abstract : We study the Euler equations with gravitational source terms derived from a potential which satisfies Poisson's equation for gravity. An adequate treatment of the source terms is achieved by introducing their discretization into an approximate Riemann solver, relying on a relaxation strategy. The associated numerical scheme is then presented and its performance demonstrated. The new method provides a straightforward extension to multidimensions and is applied to different types of problems under gravitational influence, including a one dimensional hydrostatic atmosphere and a three-dimensional Rayleigh-Taylor instability. We show the first results for the implicit version of the scheme, essential for many applications of physical interest and implemented in the code HERACLES.
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https://hal.inria.fr/hal-01103523
Contributor : Jeaniffer Vides <>
Submitted on : Wednesday, January 14, 2015 - 7:34:50 PM
Last modification on : Thursday, January 24, 2019 - 1:22:49 AM

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Jeaniffer Vides, Serge van Criekingen, Edouard Audit, Mikolaj Szydlarski. A Godunov-Type Solver for Gravitational Flows: Towards a Time-Implicit Version in the HERACLES Code. ASP Conference Series, Sep 2014, Biarritz, France. pp.279-284. ⟨hal-01103523⟩

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