A domain-decomposition method to implement electrostatic free boundary conditions in the radial direction for electric discharges

At high pressure electric discharges typically grow as thin, elongated filaments. In a numerical simulation this large aspect ratio should ideally translate into a narrow, cylindrical computational domain that envelops the discharge as closely as possible. However, the development of the discharge i...

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Detalles Bibliográficos
Autores: Malagón Romero, Alejandro, Luque, Alejandro
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2018
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/163883
Acceso en línea:http://hdl.handle.net/10261/163883
Access Level:acceso abierto
Palabra clave:Electric discharge
Streamer
Domain decomposition
Poisson equation
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spelling A domain-decomposition method to implement electrostatic free boundary conditions in the radial direction for electric dischargesMalagón Romero, AlejandroLuque, AlejandroElectric dischargeStreamerDomain decompositionPoisson equationAt high pressure electric discharges typically grow as thin, elongated filaments. In a numerical simulation this large aspect ratio should ideally translate into a narrow, cylindrical computational domain that envelops the discharge as closely as possible. However, the development of the discharge is driven by electrostatic interactions and, if the computational domain is not wide enough, the boundary conditions imposed to the electrostatic potential on the external boundary have a strong effect on the discharge. Most numerical codes circumvent this problem by either using a wide computational domain or by calculating the boundary conditions by integrating the Green's function of an infinite domain. Here we describe an accurate and efficient method to impose free boundary conditions in the radial direction for an elongated electric discharge. To facilitate the use of our method we provide a sample implementation. Finally, we apply the method to solve Poisson's equation in cylindrical coordinates with free boundary conditions in both radial and longitudinal directions. This case is of particular interest for the initial stages of discharges in long gaps or natural discharges in the atmosphere, where it is not practical to extend the simulation volume to be bounded by two electrodes. Program summary: Program Title: poisson_sparse_fft.py Program Files doi: http://dx.doi.org/10.17632/x7f6czrnsh.1 Licensing provisions: CC By 4.0 Programming language: Python Nature of problem: Electric discharges are typically elongated and their optimal computational domain has a large aspect ratio. However, the electrostatic interactions within the discharge volume may be affected by the boundary conditions imposed to the Poisson equation. Computing these boundary conditions using a direct integration of Green's function involves either heavy computations or a loss of accuracy. Solution method: We use a Domain Decomposition Method to efficiently impose free boundary conditions to the Poisson equation. This code provides a stand-alone example implementation. © 2018 The Author(s)This work was supported by the European Research Council (ERC) under the European Union H2020 programme/ERC grant agreement 681257Peer reviewedElsevierEuropean Research CouncilConsejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]201820182018info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Publisher's versioninfo:eu-repo/semantics/publishedVersionhttp://hdl.handle.net/10261/163883reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/EC/H2020/681257http://dx.doi.org/10.1016/j.cpc.2018.01.003Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/1638832026-05-22T06:33:51Z
dc.title.none.fl_str_mv A domain-decomposition method to implement electrostatic free boundary conditions in the radial direction for electric discharges
title A domain-decomposition method to implement electrostatic free boundary conditions in the radial direction for electric discharges
spellingShingle A domain-decomposition method to implement electrostatic free boundary conditions in the radial direction for electric discharges
Malagón Romero, Alejandro
Electric discharge
Streamer
Domain decomposition
Poisson equation
title_short A domain-decomposition method to implement electrostatic free boundary conditions in the radial direction for electric discharges
title_full A domain-decomposition method to implement electrostatic free boundary conditions in the radial direction for electric discharges
title_fullStr A domain-decomposition method to implement electrostatic free boundary conditions in the radial direction for electric discharges
title_full_unstemmed A domain-decomposition method to implement electrostatic free boundary conditions in the radial direction for electric discharges
title_sort A domain-decomposition method to implement electrostatic free boundary conditions in the radial direction for electric discharges
dc.creator.none.fl_str_mv Malagón Romero, Alejandro
Luque, Alejandro
author Malagón Romero, Alejandro
author_facet Malagón Romero, Alejandro
Luque, Alejandro
author_role author
author2 Luque, Alejandro
author2_role author
dc.contributor.none.fl_str_mv European Research Council
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Electric discharge
Streamer
Domain decomposition
Poisson equation
topic Electric discharge
Streamer
Domain decomposition
Poisson equation
description At high pressure electric discharges typically grow as thin, elongated filaments. In a numerical simulation this large aspect ratio should ideally translate into a narrow, cylindrical computational domain that envelops the discharge as closely as possible. However, the development of the discharge is driven by electrostatic interactions and, if the computational domain is not wide enough, the boundary conditions imposed to the electrostatic potential on the external boundary have a strong effect on the discharge. Most numerical codes circumvent this problem by either using a wide computational domain or by calculating the boundary conditions by integrating the Green's function of an infinite domain. Here we describe an accurate and efficient method to impose free boundary conditions in the radial direction for an elongated electric discharge. To facilitate the use of our method we provide a sample implementation. Finally, we apply the method to solve Poisson's equation in cylindrical coordinates with free boundary conditions in both radial and longitudinal directions. This case is of particular interest for the initial stages of discharges in long gaps or natural discharges in the atmosphere, where it is not practical to extend the simulation volume to be bounded by two electrodes. Program summary: Program Title: poisson_sparse_fft.py Program Files doi: http://dx.doi.org/10.17632/x7f6czrnsh.1 Licensing provisions: CC By 4.0 Programming language: Python Nature of problem: Electric discharges are typically elongated and their optimal computational domain has a large aspect ratio. However, the electrostatic interactions within the discharge volume may be affected by the boundary conditions imposed to the Poisson equation. Computing these boundary conditions using a direct integration of Green's function involves either heavy computations or a loss of accuracy. Solution method: We use a Domain Decomposition Method to efficiently impose free boundary conditions to the Poisson equation. This code provides a stand-alone example implementation. © 2018 The Author(s)
publishDate 2018
dc.date.none.fl_str_mv 2018
2018
2018
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Publisher's version
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/163883
url http://hdl.handle.net/10261/163883
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
info:eu-repo/grantAgreement/EC/H2020/681257
http://dx.doi.org/10.1016/j.cpc.2018.01.003
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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