A Stochastic Projection Method for Fluid Flow: II. Random Process

An uncertainty quantification scheme is developed for the simulation of stochastic thermofluid processes. The scheme relies on spectral representation of uncertainty using the polynomial chaos (PC) system. The solver combines a Galerkin procedure for the determination of PC coefficients with a projection method for efficiently simulating the resulting system of coupled transport equations. Implementation of the numerical scheme is illustrated through simulations of natural convection in a 2D square cavity with stochastic temperature distribution at the cold wall. The properties of the uncertainty representation scheme are analyzed, and the predictions are contrasted with results obtained using a Monte Carlo approach.