A stochastic Galerkin method with adaptive time-stepping for the Navier–Stokes equations
Files
Metadata
Show full item recordDate
2022-07-29Type of Work
20 pagesText
journal articles
preprints
Citation of Original Publication
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.Rights
This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.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.