| Richard M. Propp | Phillip Colella |
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Flows through porous media are characterized by localized phenomena such as fronts. To concentrate computational effort around these localized phenomena, we use Adaptive Mesh Refinement (AMR) techniques developed by Berger and Oliger. We refine in space using a nested hierarchy of block-structured grids. We refine in time by using subcycling -- we advance finer grids several times and synchronize them with the coarser grids. We introduce three new innovations in our adaptive algorithm. First, we use a volume-discrepancy method to correct for the lack of freestream preservation at coarse/fine interfaces. Second, we introduce a lagged correction scheme for coarse/fine boundary conditions to minimize the number of multilevel elliptic solves. Finally, we determine refined regions using an estimate of the local truncation error; this is a generic method of tagging cells that is suitable for the hyperbolic-elliptic problem that we are solving. Our results demonstrate that the adaptive mesh refinement algorithm is able to reproduce the results from a single-grid code with a substantial savings in memory and computational effort.