an:05264658
Zbl 1137.65393
Bürger, Raimund; Ruiz, Ricardo; Schneider, Kai; Sepúlveda, Mauricio A.
Fully adaptive multiresolution schemes for strongly degenerate parabolic equations with discontinuous flux
EN
J. Eng. Math. 60, No. 3-4, 365-385 (2008).
0022-0833 1573-2703
2008
j
65M06 35K55 35K65 90B20
discontinuous flux; multiresolution schemes; strongly degenerate parabolic equations; thresholded wavelet transform; thresholding strategy; numerical examples; finite volume discretization; Engquist-Osher approximation; traffic flow
Summary: 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.