A stochastic projection method for fluid flow I. Basic formulation

We describe the construction and implementation of a stochastic Navier-Stok es solver. The solver combines a spectral stochastic uncertainty representa tion scheme with a finite difference projection method for flow simulation. The uncertainty quantification scheme is adapted from the spectral stochas tic finite element method (SSFEM), which is based on regarding uncertainty as generating a new dimension and the solution as being dependent on this d imension. In the SSFEM formalism, the stochastic dependence is represented in terms of the polynomial chaos system, and the coefficients in the corres ponding spectral representation are obtained using a Galerkin approach. It is shown that incorporation of the spectral uncertainty representation sche me into the projection method results in a coupled system of advection-diff usion equations for the various uncertainty fields, and in a decoupled syst em of pressure projection steps. This leads to a very efficient stochastic solver, whose advantages are illustrated using steady and transient simulat ions of transport and mixing in a microchannel. (C) 2001 Academic Press.