A low-Mach Roe-type solver for the Euler equations allowing for gravity source terms *

A low-Mach Roe-type solver for the Euler equations allowing for gravity source terms *

In order to perform simulations of low Mach number flow in presence of gravity the technique from [23] is found insufficient as it is unable to cope with the presence of a hydrostatic equilibrium. Instead, a new modification of the diffusion matrix in the context of Roe-type schemes is suggested. We...

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Main Authors: Barsukow Wasilij, Edelmann Philipp V.F., Klingenberg Christian, Röpke Friedrich K.
Format: Article
Language:English
Published: EDP Sciences 2017-01-01
Series:ESAIM: Proceedings and Surveys
Online Access:https://doi.org/10.1051/proc/201758027
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spelling doaj-43fc38b932e14432858ccf4b6a82f7a52021-08-03T12:34:54ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592017-01-0158273910.1051/proc/201758027proc17582A low-Mach Roe-type solver for the Euler equations allowing for gravity source terms *Barsukow WasilijEdelmann Philipp V.F.Klingenberg ChristianRöpke Friedrich K.In order to perform simulations of low Mach number flow in presence of gravity the technique from [23] is found insufficient as it is unable to cope with the presence of a hydrostatic equilibrium. Instead, a new modification of the diffusion matrix in the context of Roe-type schemes is suggested. We show that without gravity it is able to resolve the incompressible limit, and does not violate the conditions of hydrostatic equilibrium when gravity is present. These properties are verified by performing a formal asymptotic analysis of the scheme. Furthermore, we study its von Neumann stability when subject to explicit time integration and demonstrate its abilities on numerical examples.https://doi.org/10.1051/proc/201758027
collection DOAJ
language English
format Article
sources DOAJ
author Barsukow Wasilij
Edelmann Philipp V.F.
Klingenberg Christian
Röpke Friedrich K.
spellingShingle Barsukow Wasilij
Edelmann Philipp V.F.
Klingenberg Christian
Röpke Friedrich K.
A low-Mach Roe-type solver for the Euler equations allowing for gravity source terms *
ESAIM: Proceedings and Surveys
author_facet Barsukow Wasilij
Edelmann Philipp V.F.
Klingenberg Christian
Röpke Friedrich K.
author_sort Barsukow Wasilij
title A low-Mach Roe-type solver for the Euler equations allowing for gravity source terms *
title_short A low-Mach Roe-type solver for the Euler equations allowing for gravity source terms *
title_full A low-Mach Roe-type solver for the Euler equations allowing for gravity source terms *
title_fullStr A low-Mach Roe-type solver for the Euler equations allowing for gravity source terms *
title_full_unstemmed A low-Mach Roe-type solver for the Euler equations allowing for gravity source terms *
title_sort low-mach roe-type solver for the euler equations allowing for gravity source terms *
publisher EDP Sciences
series ESAIM: Proceedings and Surveys
issn 2267-3059
publishDate 2017-01-01
description In order to perform simulations of low Mach number flow in presence of gravity the technique from [23] is found insufficient as it is unable to cope with the presence of a hydrostatic equilibrium. Instead, a new modification of the diffusion matrix in the context of Roe-type schemes is suggested. We show that without gravity it is able to resolve the incompressible limit, and does not violate the conditions of hydrostatic equilibrium when gravity is present. These properties are verified by performing a formal asymptotic analysis of the scheme. Furthermore, we study its von Neumann stability when subject to explicit time integration and demonstrate its abilities on numerical examples.
url https://doi.org/10.1051/proc/201758027
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