Monday, 11 October 2004 - 5:10 PM

This presentation is part of : Torquato Symposium

Application of Wavelet Transformations to Computing Flow and Transport Properties of Heterogeneous Media

Muhammad Sahimi, University of Southern California, University of Southern California, 925 Bloom Walk, HED 216, Los Angeles, CA 90089-1211

Computing the effective flow and transport properties of heterogeneous media, such as composite materials and porous media, is often hampered by the fact that, due to the heterogeneities and the existence of extended correlations in such media, the computational grid must have a very detailed structure. As a result, a very large set of equations, obtained from discretization of the governing equations over the domain of the problem, must be solved. Computing time-dependent properties is even more difficult, as one must solve the very large set of equations repeatedly over an extended time period. We describe a novel method, based on the use of wavelet transformations, that reduces the computations by orders of magnitude. Starting with a fine-scale computational grid that may contain millions of grid points or blocks, wavelet transformations are utilized to systematically coarsen the grid in those zones where the detailed structure of the grid may not be needed, but preserve the grid's fine structure in those zones that contribute significantly to the flow or transport process. The coarsening can be static; alternatively, it can be dynamic with the grid structure evolving with the time. We present the results of extensive computer simulations of conduction in and deformation of model heterogeneous materials to demonstrate the accuracy and efficiency of the proposed method.

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