Stochastic Galerkin methods for the steadystate Navier–Stokes equations
We study the steadystate 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]}
;
^{[2]}
 Univ. of Maryland Baltimore County (UMBC), Baltimore, MD (United States)
 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 00219991
 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 steadystate 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 steadystate 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 steadystate 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 steadystate Navier–Stokes equations},
author = {Sousedík, Bedřich and Elman, Howard C.},
abstractNote = {We study the steadystate 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}
}