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 numerica...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2014-09-01
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| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | http://dx.doi.org/10.1051/proc/201445054 |
| _version_ | 1797965694015373312 |
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| author | Vides Jeaniffer Audit Edouard Nkonga Boniface |
| author_facet | Vides Jeaniffer Audit Edouard Nkonga Boniface |
| author_sort | Vides Jeaniffer |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T02:03:54Z |
| format | Article |
| id | doaj.art-753744e4b53a4272a195c7ed465f3781 |
| institution | Directory Open Access Journal |
| issn | 2267-3059 |
| language | English |
| last_indexed | 2024-04-11T02:03:54Z |
| publishDate | 2014-09-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ESAIM: Proceedings and Surveys |
| spelling | doaj.art-753744e4b53a4272a195c7ed465f37812023-01-03T03:32:04ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592014-09-014552353210.1051/proc/201445054proc144554A relaxation scheme for inviscid flows under gravitational influenceVides Jeaniffer0Audit Edouard1Nkonga Boniface2Inria, Maison de la SimulationCEA, Maison de la SimulationUniversité de Nice-Sophia AntipolisMany 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.http://dx.doi.org/10.1051/proc/201445054 |
| spellingShingle | Vides Jeaniffer Audit Edouard Nkonga Boniface A relaxation scheme for inviscid flows under gravitational influence ESAIM: Proceedings and Surveys |
| title | A relaxation scheme for inviscid flows under gravitational
influence |
| title_full | A relaxation scheme for inviscid flows under gravitational
influence |
| title_fullStr | A relaxation scheme for inviscid flows under gravitational
influence |
| title_full_unstemmed | A relaxation scheme for inviscid flows under gravitational
influence |
| title_short | A relaxation scheme for inviscid flows under gravitational
influence |
| title_sort | relaxation scheme for inviscid flows under gravitational influence |
| url | http://dx.doi.org/10.1051/proc/201445054 |
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