An efficient fully explicit scheme for stochastic Navier-Stokes equations driven by multiplicative noise

TL;DR

This paper introduces a novel explicit pressure-correction scheme for 2D stochastic Navier-Stokes equations with multiplicative noise, achieving unconditional stability and efficiency by solving simple Poisson equations at each step.

Contribution

It is the first to apply the auxiliary variable method to stochastic Navier-Stokes equations, providing a fully explicit, stable, and efficient numerical scheme with convergence analysis.

Findings

Scheme is unconditionally stable and explicit.

Requires solving only Poisson equations with constant coefficients.

Provides strong convergence analysis for the proposed method.

Abstract

This work proposes an efficient, linear, and fully decoupled pressure-correction scheme for the 2D stochastic Navier-Stokes equations with multiplicative noise and Dirichlet boundary condition. Leveraging the auxiliary variable approach, the scheme is fully explicit yet unconditionally stable. At each time step, it only requires solving Poisson-type equations with constant coefficients. To the best of our knowledge, this is the first application of the auxiliary variable method to stochastic Navier-Stokes equations. We provide a detailed strong convergence analysis for the linearized equation under standard assumptions.