UNCERTAINTY QUANTIFICATION FOR NATURAL CONVECTION IN RANDOM POROUS MEDIA WITH INTRUSIVE POLYNOMIAL CHAOS EXPANSION

Abstract

The paper presents a framework for the construction of a stochastic projection method for the natural convection in random porous media under the local thermal nonequilibrium conditions. In this approach, the input stochastic field (porosity) is represented by the Karhunen−Loeve expansion and the output fields (e.g., velocity, pressure, fluid phase temperature, and solid phase temperature) are expressed by the polynomial chaos expansion. Using the spectral decomposition, the stochastic problem in random porous media is reformulated to a set of deterministic problems to be solved for each polynomial chaos. A stochastic projection method is implemented to obtain the chaos coefficients in the corresponding deterministic governing equations and the statistics of the numerical solution is obtained. The prediction results are compared against results obtained using a Monte Carlo method. Excellent agreement between these results indicates the efficiency and accuracy of the proposed method.