Model reduction based on proper generalized decomposition for the stochastic steady incompressible navier-stokes equations

L. Tamellini, O. Le Maître, A. Nouy

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

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).

Original languageEnglish (US)
Pages (from-to)A1089-A1117
JournalSIAM Journal on Scientific Computing
Volume36
Issue number3
DOIs
StatePublished - 2014

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

Keywords

  • Galerkin method
  • Model reduction
  • Reduced basis
  • Stochastic navier-stokes equations
  • Uncertainty quantification

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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