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

TL;DR

This paper introduces a fully adaptive multiresolution finite volume scheme for strongly degenerate parabolic equations with discontinuous flux, improving computational efficiency and data management.

Contribution

The paper presents a novel adaptive multiresolution scheme utilizing a dynamic graded tree for data compression and navigation in solving complex degenerate parabolic equations.

Findings

Enhanced computational efficiency demonstrated in traffic flow models

Effective data compression via dynamic graded tree structure

Applicable to complex models like clarifier-thickener systems

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.