Semi-implicit formulations of the Navier-Stokes equations: application to nonhydrostatic atmospheric modeling

We present semi-implicit (implicit-explicit) formulations of the compressible Navier-Stokes equations (NSE) for applications in nonhydrostatic atmospheric modeling. The compressible NSE in nonhydrostatic atmospheric modeling include buoyancy terms that require special handling if one wishes to extra...

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Detalles Bibliográficos
Autores: Giraldo, Francis Xavier, Restelli, Marco, Laeuter, Matthias
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2010
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/56382
Acceso en línea:http://hdl.handle.net/11441/56382
https://doi.org/10.1137/090775889
Access Level:acceso abierto
Palabra clave:Compressible flow
Element-based Galerkin methods
Euler
Implicit-explicit
Lagrange
Legendre
Navier-Stokes
Nonhydrostatic
Spectral elements
Time-integration
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spelling Semi-implicit formulations of the Navier-Stokes equations: application to nonhydrostatic atmospheric modelingGiraldo, Francis XavierRestelli, MarcoLaeuter, MatthiasCompressible flowElement-based Galerkin methodsEulerImplicit-explicitLagrangeLegendreNavier-StokesNonhydrostaticSpectral elementsTime-integrationWe present semi-implicit (implicit-explicit) formulations of the compressible Navier-Stokes equations (NSE) for applications in nonhydrostatic atmospheric modeling. The compressible NSE in nonhydrostatic atmospheric modeling include buoyancy terms that require special handling if one wishes to extract the Schur complement form of the linear implicit problem. We present results for five different forms of the compressible NSE and describe in detail how to formulate the semi-implicit time-integration method for these equations. Finally, we compare all five equations and compare the semi-implicit formulations of these equations both using the Schur and No Schur forms against an explicit Runge-Kutta method. Our simulations show that, if efficiency is the main criterion, it matters which form of the governing equations you choose. Furthermore, the semi-implicit formulations are faster than the explicit Runge-Kutta method for all the tests studied, especially if the Schur form is used. While we have used the spectral element method for discretizing the spatial operators, the semi-implicit formulations that we derive are directly applicable to all other numerical methods. We show results for our five semi-implicit models for a variety of problems of interest in nonhydrostatic atmospheric modeling, including inertia-gravity waves, density current (i.e., Kelvin-Helmholtz instabilities), and mountain test cases; the latter test case requires the implementation of nonreflecting boundary conditions. Therefore, we show results for all five semi-implicit models using the appropriate boundary conditions required in nonhydrostatic atmospheric modeling: no-flux (reflecting) and nonreflecting boundary conditions (NRBCs). It is shown that the NRBCs exert a strong impact on the accuracy and efficiency of the models.Office of Naval ResearchJunta de AndalucíaGerman Research FoundationSociety for Industrial and Applied MathematicsEcuaciones Diferenciales y Análisis Numérico2010info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/56382https://doi.org/10.1137/090775889reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésSIAM Journal on Scientific Computing, 32 (6), 3394-3425.PE-0602435NP07-FQM-02538LA2455/1-1http://epubs.siam.org/doi/pdf/10.1137/090775889info:eu-repo/semantics/openAccessoai:idus.us.es:11441/563822026-06-17T12:51:07Z
dc.title.none.fl_str_mv Semi-implicit formulations of the Navier-Stokes equations: application to nonhydrostatic atmospheric modeling
title Semi-implicit formulations of the Navier-Stokes equations: application to nonhydrostatic atmospheric modeling
spellingShingle Semi-implicit formulations of the Navier-Stokes equations: application to nonhydrostatic atmospheric modeling
Giraldo, Francis Xavier
Compressible flow
Element-based Galerkin methods
Euler
Implicit-explicit
Lagrange
Legendre
Navier-Stokes
Nonhydrostatic
Spectral elements
Time-integration
title_short Semi-implicit formulations of the Navier-Stokes equations: application to nonhydrostatic atmospheric modeling
title_full Semi-implicit formulations of the Navier-Stokes equations: application to nonhydrostatic atmospheric modeling
title_fullStr Semi-implicit formulations of the Navier-Stokes equations: application to nonhydrostatic atmospheric modeling
title_full_unstemmed Semi-implicit formulations of the Navier-Stokes equations: application to nonhydrostatic atmospheric modeling
title_sort Semi-implicit formulations of the Navier-Stokes equations: application to nonhydrostatic atmospheric modeling
dc.creator.none.fl_str_mv Giraldo, Francis Xavier
Restelli, Marco
Laeuter, Matthias
author Giraldo, Francis Xavier
author_facet Giraldo, Francis Xavier
Restelli, Marco
Laeuter, Matthias
author_role author
author2 Restelli, Marco
Laeuter, Matthias
author2_role author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
dc.subject.none.fl_str_mv Compressible flow
Element-based Galerkin methods
Euler
Implicit-explicit
Lagrange
Legendre
Navier-Stokes
Nonhydrostatic
Spectral elements
Time-integration
topic Compressible flow
Element-based Galerkin methods
Euler
Implicit-explicit
Lagrange
Legendre
Navier-Stokes
Nonhydrostatic
Spectral elements
Time-integration
description We present semi-implicit (implicit-explicit) formulations of the compressible Navier-Stokes equations (NSE) for applications in nonhydrostatic atmospheric modeling. The compressible NSE in nonhydrostatic atmospheric modeling include buoyancy terms that require special handling if one wishes to extract the Schur complement form of the linear implicit problem. We present results for five different forms of the compressible NSE and describe in detail how to formulate the semi-implicit time-integration method for these equations. Finally, we compare all five equations and compare the semi-implicit formulations of these equations both using the Schur and No Schur forms against an explicit Runge-Kutta method. Our simulations show that, if efficiency is the main criterion, it matters which form of the governing equations you choose. Furthermore, the semi-implicit formulations are faster than the explicit Runge-Kutta method for all the tests studied, especially if the Schur form is used. While we have used the spectral element method for discretizing the spatial operators, the semi-implicit formulations that we derive are directly applicable to all other numerical methods. We show results for our five semi-implicit models for a variety of problems of interest in nonhydrostatic atmospheric modeling, including inertia-gravity waves, density current (i.e., Kelvin-Helmholtz instabilities), and mountain test cases; the latter test case requires the implementation of nonreflecting boundary conditions. Therefore, we show results for all five semi-implicit models using the appropriate boundary conditions required in nonhydrostatic atmospheric modeling: no-flux (reflecting) and nonreflecting boundary conditions (NRBCs). It is shown that the NRBCs exert a strong impact on the accuracy and efficiency of the models.
publishDate 2010
dc.date.none.fl_str_mv 2010
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/56382
https://doi.org/10.1137/090775889
url http://hdl.handle.net/11441/56382
https://doi.org/10.1137/090775889
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv SIAM Journal on Scientific Computing, 32 (6), 3394-3425.
PE-0602435N
P07-FQM-02538
LA2455/1-1
http://epubs.siam.org/doi/pdf/10.1137/090775889
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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