Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES.
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| Title: | Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES. |
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| Authors: | Marras, Simone1 smarras@stanford.edu, Nazarov, Murtazo2, Giraldo, Francis X.1 |
| Source: | Journal of Computational Physics. Nov2015, Vol. 301, p77-101. 25p. |
| Subjects: | Galerkin methods, Spectral element method, Approximation theory, Euler equations, Finite element method, Compressible flow, Mach number |
| Abstract: | The high order spectral element approximation of the Euler equations is stabilized via a dynamic sub-grid scale model (Dyn-SGS). This model was originally designed for linear finite elements to solve compressible flows at large Mach numbers. We extend its application to high-order spectral elements to solve the Euler equations of low Mach number stratified flows. The major justification of this work is twofold: stabilization and large eddy simulation are achieved via one scheme only. Because the diffusion coefficients of the regularization stresses obtained via Dyn-SGS are residual-based, the effect of the artificial diffusion is minimal in the regions where the solution is smooth. The direct consequence is that the nominal convergence rate of the high-order solution of smooth problems is not degraded. To our knowledge, this is the first application in atmospheric modeling of a spectral element model stabilized by an eddy viscosity scheme that, by construction, may fulfill stabilization requirements, can model turbulence via LES, and is completely free of a user-tunable parameter. From its derivation, it will be immediately clear that Dyn-SGS is independent of the numerical method; it could be implemented in a discontinuous Galerkin, finite volume, or other environments alike. Preliminary discontinuous Galerkin results are reported as well. The straightforward extension to non-linear scalar problems is also described. A suite of 1D, 2D, and 3D test cases is used to assess the method, with some comparison against the results obtained with the most known Lilly–Smagorinsky SGS model. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 110009354 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Marras%2C+Simone%22">Marras, Simone</searchLink><relatesTo>1</relatesTo><i> smarras@stanford.edu</i><br /><searchLink fieldCode="AR" term="%22Nazarov%2C+Murtazo%22">Nazarov, Murtazo</searchLink><relatesTo>2</relatesTo><br /><searchLink fieldCode="AR" term="%22Giraldo%2C+Francis+X%2E%22">Giraldo, Francis X.</searchLink><relatesTo>1</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Computational+Physics%22">Journal of Computational Physics</searchLink>. Nov2015, Vol. 301, p77-101. 25p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Galerkin+methods%22">Galerkin methods</searchLink><br /><searchLink fieldCode="DE" term="%22Spectral+element+method%22">Spectral element method</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Euler+equations%22">Euler equations</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Compressible+flow%22">Compressible flow</searchLink><br /><searchLink fieldCode="DE" term="%22Mach+number%22">Mach number</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The high order spectral element approximation of the Euler equations is stabilized via a dynamic sub-grid scale model (Dyn-SGS). This model was originally designed for linear finite elements to solve compressible flows at large Mach numbers. We extend its application to high-order spectral elements to solve the Euler equations of low Mach number stratified flows. The major justification of this work is twofold: stabilization and large eddy simulation are achieved via one scheme only. Because the diffusion coefficients of the regularization stresses obtained via Dyn-SGS are residual-based, the effect of the artificial diffusion is minimal in the regions where the solution is smooth. The direct consequence is that the nominal convergence rate of the high-order solution of smooth problems is not degraded. To our knowledge, this is the first application in atmospheric modeling of a spectral element model stabilized by an eddy viscosity scheme that, by construction, may fulfill stabilization requirements, can model turbulence via LES, and is completely free of a user-tunable parameter. From its derivation, it will be immediately clear that Dyn-SGS is independent of the numerical method; it could be implemented in a discontinuous Galerkin, finite volume, or other environments alike. Preliminary discontinuous Galerkin results are reported as well. The straightforward extension to non-linear scalar problems is also described. A suite of 1D, 2D, and 3D test cases is used to assess the method, with some comparison against the results obtained with the most known Lilly–Smagorinsky SGS model. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.jcp.2015.07.034 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 25 StartPage: 77 Subjects: – SubjectFull: Galerkin methods Type: general – SubjectFull: Spectral element method Type: general – SubjectFull: Approximation theory Type: general – SubjectFull: Euler equations Type: general – SubjectFull: Finite element method Type: general – SubjectFull: Compressible flow Type: general – SubjectFull: Mach number Type: general Titles: – TitleFull: Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Marras, Simone – PersonEntity: Name: NameFull: Nazarov, Murtazo – PersonEntity: Name: NameFull: Giraldo, Francis X. IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 11 Text: Nov2015 Type: published Y: 2015 Identifiers: – Type: issn-print Value: 00219991 Numbering: – Type: volume Value: 301 Titles: – TitleFull: Journal of Computational Physics Type: main |
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