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

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:
ORCiD logo [1] ;  [2]
  1. Univ. of Maryland Baltimore County (UMBC), Baltimore, MD (United States)
  2. Univ. of Maryland, College Park, MD (United States)
Publication Date:
Grant/Contract Number:
SC0009301; DMS1521563; DMS1418754
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
Research Org:
Univ. of Maryland, College Park, MD (United States)
Sponsoring Org:
National Science Foundation (NSF); USDOE
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Stochastic Galerkin methods; Navier–Stokes equations; Uncertainty quantification
OSTI Identifier:
1418535
Alternate Identifier(s):
OSTI ID: 1467148

Sousedík, Bedřich, and Elman, Howard C. Stochastic Galerkin methods for the steady-state Navier–Stokes equations. United States: N. p., Web. doi:10.1016/j.jcp.2016.04.013.
Sousedík, Bedřich, & Elman, Howard C. Stochastic Galerkin methods for the steady-state Navier–Stokes equations. United States. doi:10.1016/j.jcp.2016.04.013.
Sousedík, Bedřich, and Elman, Howard C. 2016. "Stochastic Galerkin methods for the steady-state Navier–Stokes equations". United States. doi:10.1016/j.jcp.2016.04.013. https://www.osti.gov/servlets/purl/1418535.
@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 = {2016},
month = {4}
}