Stochastic Galerkin methods for the steady-state Navier–Stokes equations

Sousedík, Bedřich; Elman, Howard C.

doi:10.1016/j.jcp.2016.04.013

Title: Stochastic Galerkin methods for the steady-state Navier–Stokes equations

Abstract

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmark problems.

Authors:

^[1]; Elman, Howard C. ^[2]

Univ. of Maryland Baltimore County (UMBC), Baltimore, MD (United States)
Univ. of Maryland, College Park, MD (United States)

Publication Date:: Tue Apr 12 00:00:00 EDT 2016

Research Org.:: Univ. of Maryland, College Park, MD (United States)

Sponsoring Org.:: National Science Foundation (NSF); USDOE

OSTI Identifier:: 1418535

Alternate Identifier(s):: OSTI ID: 1467148

Grant/Contract Number:: SC0009301; DMS1521563; DMS1418754

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Computational Physics

Additional Journal Information:: Journal Volume: 316; Journal Issue: C; Journal ID: ISSN 0021-9991

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Stochastic Galerkin methods; Navier–Stokes equations; Uncertainty quantification

Citation Formats


                    Sousedík, Bedřich, and Elman, Howard C. Stochastic Galerkin methods for the steady-state Navier–Stokes equations.  United States: N. p., 2016. 
Web.  doi:10.1016/j.jcp.2016.04.013.

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                    Sousedík, Bedřich, & Elman, Howard C. Stochastic Galerkin methods for the steady-state Navier–Stokes equations.  United States.  https://doi.org/10.1016/j.jcp.2016.04.013

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                    Sousedík, Bedřich, and Elman, Howard C. Tue .  
"Stochastic Galerkin methods for the steady-state Navier–Stokes equations".  United States.  https://doi.org/10.1016/j.jcp.2016.04.013.  https://www.osti.gov/servlets/purl/1418535.

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@article{osti_1418535,

  title        = {Stochastic Galerkin methods for the steady-state Navier–Stokes equations},

  author       = {Sousedík, Bedřich and Elman, Howard C.},

  abstractNote = {We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmark problems.},

  doi          = {10.1016/j.jcp.2016.04.013},

  journal      = {Journal of Computational Physics},

  number       = C,

  volume       = 316,

  place        = {United States},

  year         = {Tue Apr 12 00:00:00 EDT 2016},

  month        = {Tue Apr 12 00:00:00 EDT 2016}

}

Copy to clipboard

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Works referenced in this record:

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Iterative solution of systems of linear equations arising in the context of stochastic finite elements
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Iterative Solvers for the Stochastic Finite Element Method
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Works referencing / citing this record:

An efficient algorithm for simulating ensembles of parameterized flow problems
journal, May 2018

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IMA Journal of Numerical Analysis, Vol. 39, Issue 3
DOI: 10.1093/imanum/dry029

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Title: Stochastic Galerkin methods for the steady-state Navier–Stokes equations

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