A stochastic Galerkin method with adaptive time-stepping for the Navier–Stokes equations

We study the time-dependent Navier–Stokes equations in context of stochastic finite element discretizations. Specifically, we assume that viscosity is a random field given form generalized polynomial chaos expansion, and use Galerkin method to extend methodology from Kay et al. (2010) [21] into this framework. For resulting problem, explore properties solutions, also compare results with Monte Carlo collocation. Since time-stepping scheme fully implicit, propose strategies for efficient solution linear systems using preconditioned Krylov subspace method. The effectiveness illustrated by numerical experiments.