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

Journal Article · Fri Jul 01 00:00:00 EDT 2016 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2016.04.013· OSTI ID:22572324

Sousedík, Bedřich ^[1]

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1. Department of Mathematics and Statistics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250 (United States)

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.

• OSTI ID: 22572324
• Journal Information: Journal of Computational Physics, Vol. 316; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BENCHMARKS
CHAOS THEORY
FINITE ELEMENT METHOD
NAVIER-STOKES EQUATIONS
NONLINEAR PROBLEMS
POLYNOMIALS
RANDOMNESS
STEADY-STATE CONDITIONS
STOCHASTIC PROCESSES