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Preconditioning Steady-State Navier-Stokes Equations with Random Data

Catherine E. Powell, David J. Silvester

SIAM Journal on Scientific Computing. 2012;34(5):A2482-A2506.

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Abstract

We consider the numerical solution of the steady-state Navier--Stokes equations with uncertain data. Specifically, we treat the case of uncertain viscosity, which results in a flow with an uncertain Reynolds number. After linearization, we apply a stochastic Galerkin finite element method, combining standard inf-sup stable Taylor--Hood approximation on the spatial domain (on highly stretched grids) with orthogonal polynomials in the stochastic parameter. This yields a sequence of nonsymmetric saddle-point problems with Kronecker product structure. The novel contribution of this study lies in the construction of efficient block triangular preconditioners for these discrete systems, for use with GMRES. Crucially, the preconditioners are robust with respect to the discretization and statistical parameters, and we exploit existing deterministic solvers based on the so-called pressure convection-diffusion and least-squares commutator approximations.

Bibliographic metadata

Type of resource:
Content type:
Publication type:
Publication form:
Published date:
Volume:
34
Issue:
5
Start page:
A2482
End page:
A2506
Pagination:
25
Digital Object Identifier:
10.1137/120870578
Access state:
Active

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University researcher(s):

Record metadata

Manchester eScholar ID:
uk-ac-man-scw:180067
Created by:
Silvester, David
Created:
23rd October, 2012, 13:02:24
Last modified by:
Silvester, David
Last modified:
21st November, 2012, 19:44:06