Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6932699 | Journal of Computational Physics | 2014 | 16 Pages |
Abstract
A general method to remove the numerical instability of partial differential equations is presented. Two equal terms are added to and subtracted from the right-hand side of the PDE: the first is a damping term and is treated implicitly, the second is treated explicitly. A criterion for absolute stability is found and the scheme is shown to be convergent. The method is applied with success to the mean curvature flow equation, the Kuramoto-Sivashinsky equation, and to the Rayleigh-Taylor instability in a Hele-Shaw cell, including the effect of surface tension.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Laurent Duchemin, Jens Eggers,