Model Reduction Based on Proper Generalized Decomposition for the Stochastic Steady Incompressible Navier--Stokes Equations

Handle URI:
http://hdl.handle.net/10754/598850
Title:
Model Reduction Based on Proper Generalized Decomposition for the Stochastic Steady Incompressible Navier--Stokes Equations
Authors:
Tamellini, L.; Le Maître, O.; Nouy, A.
Abstract:
In this paper we consider a proper generalized decomposition method to solve the steady incompressible Navier-Stokes equations with random Reynolds number and forcing term. The aim of such a technique is to compute a low-cost reduced basis approximation of the full stochastic Galerkin solution of the problem at hand. A particular algorithm, inspired by the Arnoldi method for solving eigenproblems, is proposed for an efficient greedy construction of a deterministic reduced basis approximation. This algorithm decouples the computation of the deterministic and stochastic components of the solution, thus allowing reuse of preexisting deterministic Navier-Stokes solvers. It has the remarkable property of only requiring the solution of m uncoupled deterministic problems for the construction of an m-dimensional reduced basis rather than M coupled problems of the full stochastic Galerkin approximation space, with m l M (up to one order of magnitudefor the problem at hand in this work). © 2014 Society for Industrial and Applied Mathematics.
Citation:
Tamellini L, Le Maître O, Nouy A (2014) Model Reduction Based on Proper Generalized Decomposition for the Stochastic Steady Incompressible Navier--Stokes Equations. SIAM Journal on Scientific Computing 36: A1089–A1117. Available: http://dx.doi.org/10.1137/120878999.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
Issue Date:
Jan-2014
DOI:
10.1137/120878999
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
This author’s work was supported by theItalian grant FIRB-IDEAS (Project RBID08223Z) “Advanced numerical techniques for uncertaintyquantification in engineering and life science problems.” He also received support from the Centerfor ADvanced MOdeling Science (CADMOS).This author’s work was partially supportedby GNR MoMaS (ANDRA, BRGM, CEA, EdF, IRSN, PACEN-CNRS) and by the French NationalResearch Agency (Grants ANR-08-JCJC-0022 and ANR-2010-BLAN-0904) and in part by the U.S.Department of Energy, Office of Advanced Scientific Computing Research, Award DE-SC0007020,and the SRI Center for Uncertainty Quantification at the King Abdullah University of Science andTechnology.This author’s work was partially supported by GNR MoMaS (ANDRA, BRGM, CEA,EdF, IRSN, PACEN-CNRS) and by the French National Research Agency (Grants ANR-08-JCJC-0022 and ANR-2010-BLAN-0904).
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Full metadata record

DC FieldValue Language
dc.contributor.authorTamellini, L.en
dc.contributor.authorLe Maître, O.en
dc.contributor.authorNouy, A.en
dc.date.accessioned2016-02-25T13:42:25Zen
dc.date.available2016-02-25T13:42:25Zen
dc.date.issued2014-01en
dc.identifier.citationTamellini L, Le Maître O, Nouy A (2014) Model Reduction Based on Proper Generalized Decomposition for the Stochastic Steady Incompressible Navier--Stokes Equations. SIAM Journal on Scientific Computing 36: A1089–A1117. Available: http://dx.doi.org/10.1137/120878999.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/120878999en
dc.identifier.urihttp://hdl.handle.net/10754/598850en
dc.description.abstractIn this paper we consider a proper generalized decomposition method to solve the steady incompressible Navier-Stokes equations with random Reynolds number and forcing term. The aim of such a technique is to compute a low-cost reduced basis approximation of the full stochastic Galerkin solution of the problem at hand. A particular algorithm, inspired by the Arnoldi method for solving eigenproblems, is proposed for an efficient greedy construction of a deterministic reduced basis approximation. This algorithm decouples the computation of the deterministic and stochastic components of the solution, thus allowing reuse of preexisting deterministic Navier-Stokes solvers. It has the remarkable property of only requiring the solution of m uncoupled deterministic problems for the construction of an m-dimensional reduced basis rather than M coupled problems of the full stochastic Galerkin approximation space, with m l M (up to one order of magnitudefor the problem at hand in this work). © 2014 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThis author’s work was supported by theItalian grant FIRB-IDEAS (Project RBID08223Z) “Advanced numerical techniques for uncertaintyquantification in engineering and life science problems.” He also received support from the Centerfor ADvanced MOdeling Science (CADMOS).This author’s work was partially supportedby GNR MoMaS (ANDRA, BRGM, CEA, EdF, IRSN, PACEN-CNRS) and by the French NationalResearch Agency (Grants ANR-08-JCJC-0022 and ANR-2010-BLAN-0904) and in part by the U.S.Department of Energy, Office of Advanced Scientific Computing Research, Award DE-SC0007020,and the SRI Center for Uncertainty Quantification at the King Abdullah University of Science andTechnology.This author’s work was partially supported by GNR MoMaS (ANDRA, BRGM, CEA,EdF, IRSN, PACEN-CNRS) and by the French National Research Agency (Grants ANR-08-JCJC-0022 and ANR-2010-BLAN-0904).en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectGalerkin methoden
dc.subjectModel reductionen
dc.subjectReduced basisen
dc.subjectStochastic navier-stokes equationsen
dc.subjectUncertainty quantificationen
dc.titleModel Reduction Based on Proper Generalized Decomposition for the Stochastic Steady Incompressible Navier--Stokes Equationsen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.contributor.institutionPolitecnico di Milano, Milan, Italyen
dc.contributor.institutionDuke University, Durham, United Statesen
dc.contributor.institutionInstitut de Recherche en Genie Civil et Mecanique, Nantes, Franceen
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