A stochastic Galerkin method for the Euler equations with Roe variable transformation

Handle URI:
http://hdl.handle.net/10754/597412
Title:
A stochastic Galerkin method for the Euler equations with Roe variable transformation
Authors:
Pettersson, Per; Iaccarino, Gianluca; Nordström, Jan
Abstract:
The Euler equations subject to uncertainty in the initial and boundary conditions are investigated via the stochastic Galerkin approach. We present a new fully intrusive method based on a variable transformation of the continuous equations. Roe variables are employed to get quadratic dependence in the flux function and a well-defined Roe average matrix that can be determined without matrix inversion.In previous formulations based on generalized polynomial chaos expansion of the physical variables, the need to introduce stochastic expansions of inverse quantities, or square roots of stochastic quantities of interest, adds to the number of possible different ways to approximate the original stochastic problem. We present a method where the square roots occur in the choice of variables, resulting in an unambiguous problem formulation.The Roe formulation saves computational cost compared to the formulation based on expansion of conservative variables. Moreover, the Roe formulation is more robust and can handle cases of supersonic flow, for which the conservative variable formulation fails to produce a bounded solution. For certain stochastic basis functions, the proposed method can be made more effective and well-conditioned. This leads to increased robustness for both choices of variables. We use a multi-wavelet basis that can be chosen to include a large number of resolution levels to handle more extreme cases (e.g. strong discontinuities) in a robust way. For smooth cases, the order of the polynomial representation can be increased for increased accuracy. © 2013 Elsevier Inc.
Citation:
Pettersson P, Iaccarino G, Nordström J (2014) A stochastic Galerkin method for the Euler equations with Roe variable transformation. Journal of Computational Physics 257: 481–500. Available: http://dx.doi.org/10.1016/j.jcp.2013.10.011.
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
Issue Date:
Jan-2014
DOI:
10.1016/j.jcp.2013.10.011
Type:
Article
ISSN:
0021-9991
Sponsors:
This work is supported by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorPettersson, Peren
dc.contributor.authorIaccarino, Gianlucaen
dc.contributor.authorNordström, Janen
dc.date.accessioned2016-02-25T12:32:42Zen
dc.date.available2016-02-25T12:32:42Zen
dc.date.issued2014-01en
dc.identifier.citationPettersson P, Iaccarino G, Nordström J (2014) A stochastic Galerkin method for the Euler equations with Roe variable transformation. Journal of Computational Physics 257: 481–500. Available: http://dx.doi.org/10.1016/j.jcp.2013.10.011.en
dc.identifier.issn0021-9991en
dc.identifier.doi10.1016/j.jcp.2013.10.011en
dc.identifier.urihttp://hdl.handle.net/10754/597412en
dc.description.abstractThe Euler equations subject to uncertainty in the initial and boundary conditions are investigated via the stochastic Galerkin approach. We present a new fully intrusive method based on a variable transformation of the continuous equations. Roe variables are employed to get quadratic dependence in the flux function and a well-defined Roe average matrix that can be determined without matrix inversion.In previous formulations based on generalized polynomial chaos expansion of the physical variables, the need to introduce stochastic expansions of inverse quantities, or square roots of stochastic quantities of interest, adds to the number of possible different ways to approximate the original stochastic problem. We present a method where the square roots occur in the choice of variables, resulting in an unambiguous problem formulation.The Roe formulation saves computational cost compared to the formulation based on expansion of conservative variables. Moreover, the Roe formulation is more robust and can handle cases of supersonic flow, for which the conservative variable formulation fails to produce a bounded solution. For certain stochastic basis functions, the proposed method can be made more effective and well-conditioned. This leads to increased robustness for both choices of variables. We use a multi-wavelet basis that can be chosen to include a large number of resolution levels to handle more extreme cases (e.g. strong discontinuities) in a robust way. For smooth cases, the order of the polynomial representation can be increased for increased accuracy. © 2013 Elsevier Inc.en
dc.description.sponsorshipThis work is supported by King Abdullah University of Science and Technology (KAUST).en
dc.publisherElsevier BVen
dc.subjectEuler equationsen
dc.subjectMulti-waveletsen
dc.subjectRoe variable transformationen
dc.subjectStochastic Galerkin methoden
dc.subjectUncertainty quantificationen
dc.titleA stochastic Galerkin method for the Euler equations with Roe variable transformationen
dc.typeArticleen
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionStanford University, Palo Alto, United Statesen
dc.contributor.institutionUppsala Universitet, Uppsala, Swedenen
dc.contributor.institutionLinkopings universitet, Linkoping, Swedenen
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