Authors: O.P. Le Maitre, O.M. Knio, R.G. Ghanem and H.N. Najm
Affilation: John's Hopkins University, United States
Pages: 246 - 249
Keywords: stochastic, polynomial chaos, projection, Navier-Stokes, uncertainty
The construction and implementaion of a stochastic flow solver is described. The solver combines a spectral stochastic uncertainty representation scheme with a finite difference projection method for flow simulation. The uncertainty quantification scheme is based on representing the stochastic dependence of the solution in terms of the Polynomial Chaos system, and hte coefficients in this representation are obtained using a Galerkin approach. It is shown that incorporation of the spectral uncertainty representation scheme into the projection method results in a coupled system of advection-diffusion equations for teh various uncertainty fields, and in a decoupled system of pressure projection steps. This leads to a very efficient stochastic solver, whose advantages are illustrated using transient simulations of transport and mixing in a microchannel.