A stochastic Galerkin method with adaptive time-stepping for the Navier–Stokes equations

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https://www.sciencedirect.com/science/article/pii/S0021999122005186?via%3Dihub

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https://doi.org/10.1016/j.jcp.2022.111456
 http://hdl.handle.net/11603/26327

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UMBC Mathematics and Statistics Department
UMBC Faculty Collection

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https://orcid.org/0000-0002-8053-8956

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2022-07-29

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journal articles
preprints
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Sousedík, Bedřich, and Randy Price. "A stochastic Galerkin method with adaptive time-stepping for the Navier–Stokes equations." Journal of Computational Physics 468 (1 November 2022). https://doi.org/10.1016/j.jcp.2022.111456.

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Abstract

We study the time-dependent 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, and we use the stochastic Galerkin method to extend the methodology from [D. A. Kay et al., SIAM J. Sci. Comput. 32(1), pp. 111–128, 2010] into this framework. For the resulting stochastic problem, we explore the properties of the resulting stochastic solutions, and we also compare the results with that of Monte Carlo and stochastic collocation. Since the time-stepping scheme is fully implicit, we also propose strategies for efficient solution of the stochastic Galerkin linear systems using a preconditioned Krylov subspace method. The effectiveness of the stochastic Galerkin method is illustrated by numerical experiments.