Layer methods for stochastic Navier–Stokes equations using simplest characteristics

We propose and study a layer method for stochastic Navier–Stokes equations (SNSE) with spatial periodic boundary conditions and additive noise. The method is constructed using conditional probabilistic representations of solutions to SNSE and exploiting ideas of the weak sense numerical integration of stochastic differential equations. We prove some convergence results for the proposed method including its first mean-square order. Results of numerical experiments on two model problems are presented.