Abstract
A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux is presented. The numerical scheme is based on a finite volume discretization using the Engquist–Osher approximation for the flux and explicit time-stepping. An adaptive multiresolution scheme with cell averages is then used to speed up CPU time and meet memory requirements. A particular feature of our scheme is the storage of the multiresolution representation of the solution in a dynamic graded tree, for the sake of data compression and to facilitate navigation. Applications to traffic flow with driver reaction and a clarifier–thickener model illustrate the efficiency of this method.
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Bürger, R., Ruiz, R., Schneider, K. et al. Fully adaptive multiresolution schemes for strongly degenerate parabolic equations with discontinuous flux. J Eng Math 60, 365–385 (2008). https://doi.org/10.1007/s10665-007-9162-6
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DOI: https://doi.org/10.1007/s10665-007-9162-6