A modified Taylor Galerkin scheme for turbulent compressible flow simulation
- Autores
- Burbridge, Horacio Pedro; Scarabino, Ana Elena; Awruch, Armando Miguel
- Año de publicación
- 2019
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- As already demonstrated by different authors, the Taylor-Galerkin (TG) scheme, in the context of the Finite Element Method (FEM), is particularly suitable for the solution of supersonic flows. The TG scheme, using hexahedral finite elements with analytical evaluation of element matrices, is applied in this work. Tools to avoid locking and a shock capturing technique for the solution of supersonic viscous and non-viscous compressible flows are also employed. However, TG scheme usually presents instabilities in subsonic flows. Even in cases in which the free stream Mach number corresponds to supersonic flows, there are always flow regions, specifically near the walls of the immersed obstacles, where the speed is lower and the local Mach number corresponds to a subsonic flow. The CharacteristicBased Split (CBS) scheme was developed in order to obtain a single method to improve the behavior with respect to TG method in subsonic and supersonic regimes. In the last two decades some works have shown advantages in convergence rates of the CBS method when compared to the TG algorithm. However, simulation time increases in the CBS method since split operations, typical of this algorithm, imply in additional element loops. In this paper a hybrid algorithm called Modified-Taylor-Galerkin scheme (MTG) is proposed. This algorithm presents advantages with respect to TG and CBS schemes in terms of convergence properties and computational processing time. In order to get an efficient algorithm, the element matrices are analytically integrated. This is performed with two different approaches. In the first approach the inverse matrix and the determinant of the Jacobian matrix at element level are evaluated with a reduced integration form, using the point located in the center of the element for mass, convective, diffusive and stabilization element matrices; all these matrices are integrated analytically. In the second approach, mass and convective matrices are calculated by a complete integration scheme (including the inverse matrix and the determinant of the Jacobian matrix at element level in the analytical expression to be integrated) and the diffusive and stabilization matrices are calculated with a reduced integration form, using the point located at the center of the element to calculate the inverse matrix and the determinant of the Jacobian matrix at element level. Finally, this work incorporates the Spalart-Allmaras (S-A) turbulence model using a conservative version of the transport equation, as proposed by the authors of the original S-A model in a later paper. Algorithms are tested to determine convergence rate improvements in both laminar and turbulent cases and for different Mach numbers (supersonic, transonic and subsonic flows).
Grupo Fluidodinámica Computacional - Materia
-
Ingeniería Aeronáutica
Compressible
Turbulent
FEM
Taylor-Galerkin
CBS
Spalart-Allmaras - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by-nc-sa/4.0/
- Repositorio
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/137595
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A modified Taylor Galerkin scheme for turbulent compressible flow simulationBurbridge, Horacio PedroScarabino, Ana ElenaAwruch, Armando MiguelIngeniería AeronáuticaCompressibleTurbulentFEMTaylor-GalerkinCBSSpalart-AllmarasAs already demonstrated by different authors, the Taylor-Galerkin (TG) scheme, in the context of the Finite Element Method (FEM), is particularly suitable for the solution of supersonic flows. The TG scheme, using hexahedral finite elements with analytical evaluation of element matrices, is applied in this work. Tools to avoid locking and a shock capturing technique for the solution of supersonic viscous and non-viscous compressible flows are also employed. However, TG scheme usually presents instabilities in subsonic flows. Even in cases in which the free stream Mach number corresponds to supersonic flows, there are always flow regions, specifically near the walls of the immersed obstacles, where the speed is lower and the local Mach number corresponds to a subsonic flow. The CharacteristicBased Split (CBS) scheme was developed in order to obtain a single method to improve the behavior with respect to TG method in subsonic and supersonic regimes. In the last two decades some works have shown advantages in convergence rates of the CBS method when compared to the TG algorithm. However, simulation time increases in the CBS method since split operations, typical of this algorithm, imply in additional element loops. In this paper a hybrid algorithm called Modified-Taylor-Galerkin scheme (MTG) is proposed. This algorithm presents advantages with respect to TG and CBS schemes in terms of convergence properties and computational processing time. In order to get an efficient algorithm, the element matrices are analytically integrated. This is performed with two different approaches. In the first approach the inverse matrix and the determinant of the Jacobian matrix at element level are evaluated with a reduced integration form, using the point located in the center of the element for mass, convective, diffusive and stabilization element matrices; all these matrices are integrated analytically. In the second approach, mass and convective matrices are calculated by a complete integration scheme (including the inverse matrix and the determinant of the Jacobian matrix at element level in the analytical expression to be integrated) and the diffusive and stabilization matrices are calculated with a reduced integration form, using the point located at the center of the element to calculate the inverse matrix and the determinant of the Jacobian matrix at element level. Finally, this work incorporates the Spalart-Allmaras (S-A) turbulence model using a conservative version of the transport equation, as proposed by the authors of the original S-A model in a later paper. Algorithms are tested to determine convergence rate improvements in both laminar and turbulent cases and for different Mach numbers (supersonic, transonic and subsonic flows).Grupo Fluidodinámica Computacional2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://sedici.unlp.edu.ar/handle/10915/137595enginfo:eu-repo/semantics/altIdentifier/issn/0213-1315info:eu-repo/semantics/altIdentifier/doi/10.23967/j.rimni.2019.09.006info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:34:54Zoai:sedici.unlp.edu.ar:10915/137595Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:34:54.91SEDICI (UNLP) - Universidad Nacional de La Platafalse |
dc.title.none.fl_str_mv |
A modified Taylor Galerkin scheme for turbulent compressible flow simulation |
title |
A modified Taylor Galerkin scheme for turbulent compressible flow simulation |
spellingShingle |
A modified Taylor Galerkin scheme for turbulent compressible flow simulation Burbridge, Horacio Pedro Ingeniería Aeronáutica Compressible Turbulent FEM Taylor-Galerkin CBS Spalart-Allmaras |
title_short |
A modified Taylor Galerkin scheme for turbulent compressible flow simulation |
title_full |
A modified Taylor Galerkin scheme for turbulent compressible flow simulation |
title_fullStr |
A modified Taylor Galerkin scheme for turbulent compressible flow simulation |
title_full_unstemmed |
A modified Taylor Galerkin scheme for turbulent compressible flow simulation |
title_sort |
A modified Taylor Galerkin scheme for turbulent compressible flow simulation |
dc.creator.none.fl_str_mv |
Burbridge, Horacio Pedro Scarabino, Ana Elena Awruch, Armando Miguel |
author |
Burbridge, Horacio Pedro |
author_facet |
Burbridge, Horacio Pedro Scarabino, Ana Elena Awruch, Armando Miguel |
author_role |
author |
author2 |
Scarabino, Ana Elena Awruch, Armando Miguel |
author2_role |
author author |
dc.subject.none.fl_str_mv |
Ingeniería Aeronáutica Compressible Turbulent FEM Taylor-Galerkin CBS Spalart-Allmaras |
topic |
Ingeniería Aeronáutica Compressible Turbulent FEM Taylor-Galerkin CBS Spalart-Allmaras |
dc.description.none.fl_txt_mv |
As already demonstrated by different authors, the Taylor-Galerkin (TG) scheme, in the context of the Finite Element Method (FEM), is particularly suitable for the solution of supersonic flows. The TG scheme, using hexahedral finite elements with analytical evaluation of element matrices, is applied in this work. Tools to avoid locking and a shock capturing technique for the solution of supersonic viscous and non-viscous compressible flows are also employed. However, TG scheme usually presents instabilities in subsonic flows. Even in cases in which the free stream Mach number corresponds to supersonic flows, there are always flow regions, specifically near the walls of the immersed obstacles, where the speed is lower and the local Mach number corresponds to a subsonic flow. The CharacteristicBased Split (CBS) scheme was developed in order to obtain a single method to improve the behavior with respect to TG method in subsonic and supersonic regimes. In the last two decades some works have shown advantages in convergence rates of the CBS method when compared to the TG algorithm. However, simulation time increases in the CBS method since split operations, typical of this algorithm, imply in additional element loops. In this paper a hybrid algorithm called Modified-Taylor-Galerkin scheme (MTG) is proposed. This algorithm presents advantages with respect to TG and CBS schemes in terms of convergence properties and computational processing time. In order to get an efficient algorithm, the element matrices are analytically integrated. This is performed with two different approaches. In the first approach the inverse matrix and the determinant of the Jacobian matrix at element level are evaluated with a reduced integration form, using the point located in the center of the element for mass, convective, diffusive and stabilization element matrices; all these matrices are integrated analytically. In the second approach, mass and convective matrices are calculated by a complete integration scheme (including the inverse matrix and the determinant of the Jacobian matrix at element level in the analytical expression to be integrated) and the diffusive and stabilization matrices are calculated with a reduced integration form, using the point located at the center of the element to calculate the inverse matrix and the determinant of the Jacobian matrix at element level. Finally, this work incorporates the Spalart-Allmaras (S-A) turbulence model using a conservative version of the transport equation, as proposed by the authors of the original S-A model in a later paper. Algorithms are tested to determine convergence rate improvements in both laminar and turbulent cases and for different Mach numbers (supersonic, transonic and subsonic flows). Grupo Fluidodinámica Computacional |
description |
As already demonstrated by different authors, the Taylor-Galerkin (TG) scheme, in the context of the Finite Element Method (FEM), is particularly suitable for the solution of supersonic flows. The TG scheme, using hexahedral finite elements with analytical evaluation of element matrices, is applied in this work. Tools to avoid locking and a shock capturing technique for the solution of supersonic viscous and non-viscous compressible flows are also employed. However, TG scheme usually presents instabilities in subsonic flows. Even in cases in which the free stream Mach number corresponds to supersonic flows, there are always flow regions, specifically near the walls of the immersed obstacles, where the speed is lower and the local Mach number corresponds to a subsonic flow. The CharacteristicBased Split (CBS) scheme was developed in order to obtain a single method to improve the behavior with respect to TG method in subsonic and supersonic regimes. In the last two decades some works have shown advantages in convergence rates of the CBS method when compared to the TG algorithm. However, simulation time increases in the CBS method since split operations, typical of this algorithm, imply in additional element loops. In this paper a hybrid algorithm called Modified-Taylor-Galerkin scheme (MTG) is proposed. This algorithm presents advantages with respect to TG and CBS schemes in terms of convergence properties and computational processing time. In order to get an efficient algorithm, the element matrices are analytically integrated. This is performed with two different approaches. In the first approach the inverse matrix and the determinant of the Jacobian matrix at element level are evaluated with a reduced integration form, using the point located in the center of the element for mass, convective, diffusive and stabilization element matrices; all these matrices are integrated analytically. In the second approach, mass and convective matrices are calculated by a complete integration scheme (including the inverse matrix and the determinant of the Jacobian matrix at element level in the analytical expression to be integrated) and the diffusive and stabilization matrices are calculated with a reduced integration form, using the point located at the center of the element to calculate the inverse matrix and the determinant of the Jacobian matrix at element level. Finally, this work incorporates the Spalart-Allmaras (S-A) turbulence model using a conservative version of the transport equation, as proposed by the authors of the original S-A model in a later paper. Algorithms are tested to determine convergence rate improvements in both laminar and turbulent cases and for different Mach numbers (supersonic, transonic and subsonic flows). |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019 |
dc.type.none.fl_str_mv |
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format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://sedici.unlp.edu.ar/handle/10915/137595 |
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dc.language.none.fl_str_mv |
eng |
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eng |
dc.relation.none.fl_str_mv |
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dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) |
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openAccess |
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http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) |
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