A low-rank solver for the Navier-Stokes equations with uncertain viscosity

Kookjin Lee, Howard C. Elman, Bedřich Sousedík

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We study an iterative low-rank approximation method for the solution of the steady-state stochastic Navier-Stokes equations with uncertain viscosity. The method is based on linearization schemes using Picard and Newton iterations and stochastic finite element discretizations of the linearized problems. For computing the low-rank approximate solution, we adapt the nonlinear iterations to an inexact and low-rank variant, where the solution of the linear system at each nonlinear step is approximated by a quantity of low rank. This is achieved by using a tensor variant of the GMRES method as a solver for the linear systems. We explore the inexact low-rank nonlinear iteration with a set of benchmark problems, using a model of ow over an obstacle, under various configurations characterizing the statistical features of the uncertain viscosity, and we demonstrate its effectiveness by extensive numerical experiments.

Original languageEnglish (US)
Pages (from-to)1275-1300
Number of pages26
JournalSIAM-ASA Journal on Uncertainty Quantification
Volume7
Issue number4
DOIs
StatePublished - 2019
Externally publishedYes

Keywords

  • Low-rank approximation
  • Navier-Stokes equations
  • Stochastic Galerkin method

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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