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arXiv · 0807.0403

Fully adaptive multiresolution schemes for strongly degenerate parabolic equations with discontinuous flux

Raimund Bürger·Ricardo Ruiz Baier·Mauricio Sepúlveda·Kai Schneider
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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 adaptivemultiresolution 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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Raimund Bürger, Ricardo Ruiz Baier, Mauricio Sepúlveda, Kai Schneider. 2008-07-02. Fully adaptive multiresolution schemes for strongly degenerate parabolic equations with discontinuous flux. https://doi.org/10.1007/s10665-007-9162-6

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