A stochastic Galerkin method with adaptive time-stepping for the Navier–Stokes equations
| dc.contributor.author | Sousedik, Bedrich | |
| dc.contributor.author | Price, Randy | |
| dc.date.accessioned | 2022-11-14T17:52:38Z | |
| dc.date.available | 2022-11-14T17:52:38Z | |
| dc.date.issued | 2022-07-29 | |
| dc.description.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. | en_US |
| dc.description.sponsorship | This work was supported by the U. S. National Science Foundation under grant DMS1913201. Most of the computations were performed at the Center for Computational Mathematics, University of Colorado Denver, and the support of Prof. Jan Mandel is greatly appreciated. Part of the work was completed while Randy Price was student at the University of Maryland, Baltimore County. | en_US |
| dc.description.uri | https://www.sciencedirect.com/science/article/pii/S0021999122005186?via%3Dihub | en_US |
| dc.format.extent | 20 pages | en_US |
| dc.genre | journal articles | en_US |
| dc.genre | preprints | en_US |
| dc.identifier | doi:10.13016/m2cqfx-6cki | |
| dc.identifier.citation | 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. | en_US |
| dc.identifier.uri | https://doi.org/10.1016/j.jcp.2022.111456 | |
| dc.identifier.uri | http://hdl.handle.net/11603/26327 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | Elsevier | en_US |
| dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
| dc.relation.ispartof | UMBC Mathematics Department Collection | |
| dc.relation.ispartof | UMBC Faculty Collection | |
| dc.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. | en_US |
| dc.title | A stochastic Galerkin method with adaptive time-stepping for the Navier–Stokes equations | en_US |
| dc.type | Text | en_US |
| dcterms.creator | https://orcid.org/0000-0002-8053-8956 | en_US |