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Mean-Square Approximation of Navier-Stokes Equations with Additive Noise in Vorticity-Velocity Formulation

Mean-Square Approximation of Navier-Stokes Equations with Additive Noise in Vorticity-Velocity Formulation

Year:    2021

Author:    M.V. Tretyakov, G.N. Milstein, M.V. Tretyakov

Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 1 : pp. 1–30

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2020-0034

Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 1 : pp. 1–30

Published online:    2021-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    30

Keywords:    Navier-Stokes equations vorticity numerical method stochastic partial differential equations mean-square convergence.

Author Details

M.V. Tretyakov

G.N. Milstein

M.V. Tretyakov

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