Hydrostatic equilibrium preservation in MHD numerical simulation with stratified atmospheres: Explicit Godunov-type schemes with MUSCL reconstruction

Autores
Krause, Gustavo Javier
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Many astrophysical processes involving plasma flows are produced in the context of a gravitationally stratified atmosphere in hydrostatic equilibrium, in which strong gradients can exist with gas properties that vary in small regions by several orders of magnitude. The standard Godunov-type schemes with polynomial reconstruction used to numerically solve these problems fail to preserve the hydrostatic equilibrium owing to the appearance of spurious fluxes generated by the numerical unbalance between gravitational forces and pressure gradients. Aims. The aim of this work is to present local hydrostatic reconstruction techniques that can be implemented in existing codes with Godunov-type methods to obtain well-balanced schemes that numerically satisfy the hydrostatic equilibrium for various conditions. Methods. The proposed numerical scheme is based on the Godunov method with second order MUSCL-type reconstruction, as is extensively used in astrophysical applications. The difference between the scheme and the standard formulations is only given by calculating the pressure and density Riemann states on each intercell face and by computing the gravitational source term on each cell. Results. The local hydrostatic reconstruction scheme is implemented in the FLASH code to verify the well-balanced property for hydrostatic equilibrium with constant or linearly variable temperature and constant or variable gravity. In addition, the behavior of the scheme for hydrostatic equilibrium with arbitrary temperature distributions is also analyzed together with the ability to propagate low-amplitude waves and to capture shock waves. Conclusions. The scheme is demonstrated to be robust and relatively simple to implement in existing codes. This approach produces good results in hydrostatic equilibrium preservation, satisfying the well-balanced property for the preset conditions and strongly reducing the spurious fluxes for extreme configurations.
Fil: Krause, Gustavo Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Estudios Avanzados en Ingeniería y Tecnología. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Estudios Avanzados en Ingeniería y Tecnología; Argentina
Materia
NUMERICAL METHODS
MAGNETOHYDRODYNAMICS (MHD)
SUN:ATMOSPHERE
SUN: GENERAL
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/121161

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network_name_str CONICET Digital (CONICET)
spelling Hydrostatic equilibrium preservation in MHD numerical simulation with stratified atmospheres: Explicit Godunov-type schemes with MUSCL reconstructionKrause, Gustavo JavierNUMERICAL METHODSMAGNETOHYDRODYNAMICS (MHD)SUN:ATMOSPHERESUN: GENERALhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Many astrophysical processes involving plasma flows are produced in the context of a gravitationally stratified atmosphere in hydrostatic equilibrium, in which strong gradients can exist with gas properties that vary in small regions by several orders of magnitude. The standard Godunov-type schemes with polynomial reconstruction used to numerically solve these problems fail to preserve the hydrostatic equilibrium owing to the appearance of spurious fluxes generated by the numerical unbalance between gravitational forces and pressure gradients. Aims. The aim of this work is to present local hydrostatic reconstruction techniques that can be implemented in existing codes with Godunov-type methods to obtain well-balanced schemes that numerically satisfy the hydrostatic equilibrium for various conditions. Methods. The proposed numerical scheme is based on the Godunov method with second order MUSCL-type reconstruction, as is extensively used in astrophysical applications. The difference between the scheme and the standard formulations is only given by calculating the pressure and density Riemann states on each intercell face and by computing the gravitational source term on each cell. Results. The local hydrostatic reconstruction scheme is implemented in the FLASH code to verify the well-balanced property for hydrostatic equilibrium with constant or linearly variable temperature and constant or variable gravity. In addition, the behavior of the scheme for hydrostatic equilibrium with arbitrary temperature distributions is also analyzed together with the ability to propagate low-amplitude waves and to capture shock waves. Conclusions. The scheme is demonstrated to be robust and relatively simple to implement in existing codes. This approach produces good results in hydrostatic equilibrium preservation, satisfying the well-balanced property for the preset conditions and strongly reducing the spurious fluxes for extreme configurations.Fil: Krause, Gustavo Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Estudios Avanzados en Ingeniería y Tecnología. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Estudios Avanzados en Ingeniería y Tecnología; ArgentinaEDP Sciences2019-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/121161Krause, Gustavo Javier; Hydrostatic equilibrium preservation in MHD numerical simulation with stratified atmospheres: Explicit Godunov-type schemes with MUSCL reconstruction; EDP Sciences; Astronomy and Astrophysics; 631; A68; 11-2019; 1-150004-63611432-0746CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1051/0004-6361/201936387info:eu-repo/semantics/altIdentifier/url/https://www.aanda.org/articles/aa/full_html/2019/11/aa36387-19/aa36387-19.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:46:53Zoai:ri.conicet.gov.ar:11336/121161instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:46:53.984CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Hydrostatic equilibrium preservation in MHD numerical simulation with stratified atmospheres: Explicit Godunov-type schemes with MUSCL reconstruction
title Hydrostatic equilibrium preservation in MHD numerical simulation with stratified atmospheres: Explicit Godunov-type schemes with MUSCL reconstruction
spellingShingle Hydrostatic equilibrium preservation in MHD numerical simulation with stratified atmospheres: Explicit Godunov-type schemes with MUSCL reconstruction
Krause, Gustavo Javier
NUMERICAL METHODS
MAGNETOHYDRODYNAMICS (MHD)
SUN:ATMOSPHERE
SUN: GENERAL
title_short Hydrostatic equilibrium preservation in MHD numerical simulation with stratified atmospheres: Explicit Godunov-type schemes with MUSCL reconstruction
title_full Hydrostatic equilibrium preservation in MHD numerical simulation with stratified atmospheres: Explicit Godunov-type schemes with MUSCL reconstruction
title_fullStr Hydrostatic equilibrium preservation in MHD numerical simulation with stratified atmospheres: Explicit Godunov-type schemes with MUSCL reconstruction
title_full_unstemmed Hydrostatic equilibrium preservation in MHD numerical simulation with stratified atmospheres: Explicit Godunov-type schemes with MUSCL reconstruction
title_sort Hydrostatic equilibrium preservation in MHD numerical simulation with stratified atmospheres: Explicit Godunov-type schemes with MUSCL reconstruction
dc.creator.none.fl_str_mv Krause, Gustavo Javier
author Krause, Gustavo Javier
author_facet Krause, Gustavo Javier
author_role author
dc.subject.none.fl_str_mv NUMERICAL METHODS
MAGNETOHYDRODYNAMICS (MHD)
SUN:ATMOSPHERE
SUN: GENERAL
topic NUMERICAL METHODS
MAGNETOHYDRODYNAMICS (MHD)
SUN:ATMOSPHERE
SUN: GENERAL
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Many astrophysical processes involving plasma flows are produced in the context of a gravitationally stratified atmosphere in hydrostatic equilibrium, in which strong gradients can exist with gas properties that vary in small regions by several orders of magnitude. The standard Godunov-type schemes with polynomial reconstruction used to numerically solve these problems fail to preserve the hydrostatic equilibrium owing to the appearance of spurious fluxes generated by the numerical unbalance between gravitational forces and pressure gradients. Aims. The aim of this work is to present local hydrostatic reconstruction techniques that can be implemented in existing codes with Godunov-type methods to obtain well-balanced schemes that numerically satisfy the hydrostatic equilibrium for various conditions. Methods. The proposed numerical scheme is based on the Godunov method with second order MUSCL-type reconstruction, as is extensively used in astrophysical applications. The difference between the scheme and the standard formulations is only given by calculating the pressure and density Riemann states on each intercell face and by computing the gravitational source term on each cell. Results. The local hydrostatic reconstruction scheme is implemented in the FLASH code to verify the well-balanced property for hydrostatic equilibrium with constant or linearly variable temperature and constant or variable gravity. In addition, the behavior of the scheme for hydrostatic equilibrium with arbitrary temperature distributions is also analyzed together with the ability to propagate low-amplitude waves and to capture shock waves. Conclusions. The scheme is demonstrated to be robust and relatively simple to implement in existing codes. This approach produces good results in hydrostatic equilibrium preservation, satisfying the well-balanced property for the preset conditions and strongly reducing the spurious fluxes for extreme configurations.
Fil: Krause, Gustavo Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Estudios Avanzados en Ingeniería y Tecnología. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Estudios Avanzados en Ingeniería y Tecnología; Argentina
description Many astrophysical processes involving plasma flows are produced in the context of a gravitationally stratified atmosphere in hydrostatic equilibrium, in which strong gradients can exist with gas properties that vary in small regions by several orders of magnitude. The standard Godunov-type schemes with polynomial reconstruction used to numerically solve these problems fail to preserve the hydrostatic equilibrium owing to the appearance of spurious fluxes generated by the numerical unbalance between gravitational forces and pressure gradients. Aims. The aim of this work is to present local hydrostatic reconstruction techniques that can be implemented in existing codes with Godunov-type methods to obtain well-balanced schemes that numerically satisfy the hydrostatic equilibrium for various conditions. Methods. The proposed numerical scheme is based on the Godunov method with second order MUSCL-type reconstruction, as is extensively used in astrophysical applications. The difference between the scheme and the standard formulations is only given by calculating the pressure and density Riemann states on each intercell face and by computing the gravitational source term on each cell. Results. The local hydrostatic reconstruction scheme is implemented in the FLASH code to verify the well-balanced property for hydrostatic equilibrium with constant or linearly variable temperature and constant or variable gravity. In addition, the behavior of the scheme for hydrostatic equilibrium with arbitrary temperature distributions is also analyzed together with the ability to propagate low-amplitude waves and to capture shock waves. Conclusions. The scheme is demonstrated to be robust and relatively simple to implement in existing codes. This approach produces good results in hydrostatic equilibrium preservation, satisfying the well-balanced property for the preset conditions and strongly reducing the spurious fluxes for extreme configurations.
publishDate 2019
dc.date.none.fl_str_mv 2019-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/121161
Krause, Gustavo Javier; Hydrostatic equilibrium preservation in MHD numerical simulation with stratified atmospheres: Explicit Godunov-type schemes with MUSCL reconstruction; EDP Sciences; Astronomy and Astrophysics; 631; A68; 11-2019; 1-15
0004-6361
1432-0746
CONICET Digital
CONICET
url http://hdl.handle.net/11336/121161
identifier_str_mv Krause, Gustavo Javier; Hydrostatic equilibrium preservation in MHD numerical simulation with stratified atmospheres: Explicit Godunov-type schemes with MUSCL reconstruction; EDP Sciences; Astronomy and Astrophysics; 631; A68; 11-2019; 1-15
0004-6361
1432-0746
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1051/0004-6361/201936387
info:eu-repo/semantics/altIdentifier/url/https://www.aanda.org/articles/aa/full_html/2019/11/aa36387-19/aa36387-19.html
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv EDP Sciences
publisher.none.fl_str_mv EDP Sciences
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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