Reconstruction of Heterogeneous Media by a Cross-Correlation Function and Graph Theory

Muhammad Sahimi
USC, USA

Abstract:
Modeling of porous materials in which the pores have irregular shapes and surface, and computing their effective transport properties, such as diffusivity, conductivity and elastic moduli are long-standing problems that have been studied for decades. The first step toward addressing the problems is developing an accurate model for the materials. One way of doing so is based on reconstruction: Given limited amount of data for an inhomogeneous material, one attempts to develop a model that not only honors the data, but also provides accurate predictions for its various properties. We describe a new multiscale reconstruction method based on a cross-correlation function and graph-theoretical concepts that is capable of generating a large number of realizations for the morphology of a given porous material. The accuracy of the method is demonstrated by applying it to reconstruction of several complex 2D and 3D examples of heterogeneous materials and computing their various morphological and transport properties. The computational cost of the method is very low and, therefore, it can generate large-size models for complex materials and upscaling them to sizes much larger than laboratory scales.