Grid coarsening, simulation of transport processes in, and scale-up of heterogeneous media: Application of multiresolution wavelet transformations

We describe a recently-developed approach to the numerical simulation of transport processes in heterogeneous materials and fluid flow in porous media. The morphology of such materials and media is characterized by broadly-distributed and correlated local conductances or permeabilities, hence necessitating its representation by a highly-resolved computational grid that may contain millions of grid points or blocks. Simulation of flow and transport in such grids is very difficult and time consuming. The new approach is based on the use of wavelet transformations. It computes the wavelet scaling and detail coefficients of the conductance or permeability field in the highly-resolved grid. It then utilizes the coefficients to systematically coarsen the grid’s low-conductance or permeability blocks while retaining its high resolution in the high-permeability or conductance zones, and those zones in which the quantities of interest, such as the temperature or pressure, experience large variations. The coarsening can be static, generating a fixed grid, but may also be dynamic such that the grid structure evolves with the time if, for example, the local conductances are a strong function of the temperature. The method is applied to study transient flow and transport in heterogeneous materials and porous media, and is shown to lead to accurate solution of the problem at greatly reduced (by at least two orders of magnitude) computational cost.