Fully adaptive multiresolution schemes for strongly degenerate parabolic equations with discontinuous flux
For researchers solving degenerate parabolic PDEs with discontinuous flux, this offers an adaptive method that improves computational efficiency.
The paper presents a fully adaptive finite volume multiresolution scheme for 1D strongly degenerate parabolic equations with discontinuous flux, achieving CPU time speedup and memory reduction. Applications to traffic flow and clarifier-thickener models demonstrate efficiency.
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.