The velocity tracking problem for Wick-stochastic Navier–Stokes flows using Weiner chaos expansion

In this paper, we numerically investigate a distributed control problem of stochastic incompressible Newtonian fluid flows modeled by Navier–Stokes equations with additive white noise. Wick product is applied to define the nonlinear convective term. The objective of optimization is to track a given deterministic or stochastic velocity field. An optimization algorithm based on Weiner chaos expansion is proposed. Numerical tests are performed to validate our methodology.