Modeling multiscale diffusion processes in random heterogeneous media

A simple stochastic up-scaling strategy is presented for incorporating the effects of micro-scale variations of thermal conductivity in the thermal analysis of macro-scale systems. Incomplete characterization of the fine-scale variation necessitates posing the thermal conductivity as a stochastic multiscale random field. A data-driven approach coupled with a non-linear dimension reduction algorithm is used to construct a low-dimensional stochastic descriptor of the fine-scale variation of the stochastic conductivity. A representative volume element (RVE) argument is utilized to construct a simple model for up-scaling the stochastic thermal conductivity. In this model, the effective stochastic thermal conductivity is estimated by virtually interrogating the stochastic RV. A realistic example of the proposed stochastic multiscale diffusion strategy is illustrated utilizing limited experimental data.