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

Raimund Büger, Ricardo Ruiz, Kai Schneider, Mauricio A. Sepúlveda

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10 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)365-385
Number of pages21
JournalJournal of Engineering Mathematics
Volume60
Issue number3-4
DOIs
Publication statusPublished - 1 Mar 2008
Externally publishedYes

Keywords

  • Discontinuous flux
  • Multiresolution schemes
  • Strongly degenerate parabolic equations
  • Thresholded wavelet transform
  • Thresholding strategy

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