G N Milstein
Mean-square approximation of Navier-Stokes equations with additive noise in vorticity-velocity formulation
Milstein, G N; Tretyakov, M V
Abstract
We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions and additive noise in the vorticity-velocity formulation. The approximation is based on freezing the velocity on time subintervals resulting in a linear stochastic parabolic equation for vorticity. At each time step, the velocity is expressed via vorticity using a formula corresponding to the Biot-Savart-type law. We prove the first mean-square convergence order of the vorticity approximation.
Citation
Milstein, G. N., & Tretyakov, M. V. (2021). Mean-square approximation of Navier-Stokes equations with additive noise in vorticity-velocity formulation. Numerical Mathematics, 14(1), 1-30. https://doi.org/10.4208/nmtma.OA-2020-0034
Journal Article Type | Article |
---|---|
Acceptance Date | Aug 27, 2020 |
Online Publication Date | Sep 14, 2020 |
Publication Date | 2021 |
Deposit Date | Sep 11, 2020 |
Publicly Available Date | Sep 14, 2020 |
Journal | NUMERICAL MATHEMATICS: Theory, Methods and Applications |
Peer Reviewed | Peer Reviewed |
Volume | 14 |
Issue | 1 |
Pages | 1-30 |
DOI | https://doi.org/10.4208/nmtma.OA-2020-0034 |
Keywords | Navier-Stokes equations; vorticity; numerical method; stochastic partial differential equa- tions; mean-square convergence |
Public URL | https://nottingham-repository.worktribe.com/output/4855421 |
Publisher URL | http://www.global-sci.org/intro/online/read?article_id=967.html |
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