Transport processes in heterogeneous media are of fundamental importance to understanding a variety of phenomena in many systems of practical interests. Examples include transport in large-scale porous media, conduction in amorphous seminconductors at low temperatures, and turbulent transport and reaction in the atmosphere. Two important characteristics of such system are that, (1) they represent multiscale systems in which the disparity between the smallest and largest length scales of importantce is many orders of magnitude, and (2) they represent highly heterogeneouis media in that, the local transport properties vary spatially and broadly over several orders of magnitude. Simulation of transport processes in such systems is highly difficult, due to their multiscale and heterogeneous nature. We describe a novel computational algorithm, based on the use of the wavelet transformations, for generation of the computational grids that are highly resolved where important information at the local scale must be preserved in the grid, while they are coarsened when such information are either not available or needed. The method results in overfive orders of magnitude speed-up in the computations. Several example are discussed.

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