Efficient quantification of the effect of uncertainties in advection-diffusion problems using polynomial chaos

摘要

Uncertainties in advection-diffusion heat transfer problems are modeled using polynomial chaos to increase the basic understanding of the effect of physical variability. The polynomial chaos method approximates the effect of uncertain parameters using a polynomial expansion in probability space. Since the computational work of an uncertainty analysis increases rapidly with the number of uncertain parameters to the equivalence of many deterministic simulations, strategies for efficient quantification of the effect of multiple uncertain parameters are needed. Three strategies are studied in this article. Results are presented for advection-diffusion problems of heat transfer in one-dimensional and two-dimensional pipe flows.