Preprint 1997-029

Front Tracking and Operator Splitting for Nonlinear Degenerate Convection-Diffusion Equations

Abstract: We describe two variants of an operator splitting strategy for nonlinear, possibly strongly degenerate, convection--diffusion equations. The strategy is based on splitting the equations into a hyperbolic conservation law for convection and a possibly degenerate parabolic equation for diffusion. The conservation law is solved by a front tracking method while the diffusion equation is here solved by a finite difference scheme. The numerical methods are unconditionally stable in the sense that the (splitting) time step is not restricted by the spatial discretization parameter. The strategy is designed to handle all combinations of convection and diffusion (including the purely hyperbolic case). Two numerical examples are presented to highlight the features of the methods, and the potential for parallel implementation is discussed.

Paper:

Available as PostScript

Title:

Front tracking and operator splitting for nonlinear degenerate convection-diffusion equations

Author(s):

Steinar Evje, mailto:steinar.evje@mi.uib.no

Kenneth Hvistendahl Karlsen, mailto:kenneth.karlsen@mi.uib.no

Knut-Andreas Lie, mailto:andreas@math.ntnu.no

Nils Henrik Risebro , mailto:nilshr@math.uio.no

Publishing information:

Preprint, Institut Mittag-Leffler, 1997, Stockholm, Sweden

Comments:

Submitted by:

mailto:andreas@math.ntnu.no November 18 1997.