Abstract

An adaptive finite volume method for one-dimensional strongly degenerate parabolic equations is presented. Using an explicit conservative numerical scheme with a third-order Runge-Kutta method for the time discretization, a third-order ENO interpolation for the convective term, and adding a conservative discretization for the diffusive term, we apply the multiresolution method combining two fundamental concepts: the switch between central interpolation or exact computing of numerical flux and a thresholded wavelet transform applied to cell averages of the solution to control the switch. Applications to mathematical models of sedimentation-consolidation processes and traffic flow with driver reaction, which involve different types of boundary conditions, illustrate the computational efficiency of the new method. © 2007 Wiley Periodicals, Inc.