Multiresolution wavelet coarsening and analysis of transport in heterogeneous media

Modeling transport in a disordered medium with broadly distributed and correlated heterogeneities has been hampered by the fact that a very large set of equations must be solved if the heterogeneities are distributed over several distinct length scales. We recently proposed a novel method based on the application of wavelet transformations (Phys. Rev. Lett. 79 (1997) 4385) that can be used for simulation of transport processes in such disordered media. In this paper, we extend the method so as to be able to study transport in two classes of highly heterogeneous media that are otherwise very difficult to simulate, namely, disordered anisotropic media, and those that contain more than one distinct family of transport paths (for example, natural rock with both pores and fractures). We report the results of extensive computer simulations of transport in such disordered media in which the heterogeneities are broadly distributed and contain long-range correlations. We show that, even for the type of disordered media that we consider in this paper, the wavelet-based method drastically reduces (by at least two orders of magnitude) the number of equations to be solved without neglecting any important information about the media's morphology, hence providing highly accurate estimates of their transport properties. Thus, we conclude that the wavelet-based method is applicable to any disordered medium with any type of heterogeneities.