A general method to remove the stiffness of PDEs

2013/08/07 by Duchemin, Laurent, Eggers, Jens
#Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1308.1621

Abstract

A new method to remove the stiffness of partial differential equations is presented. Two terms are added to the right-hand-side of the PDE : the first is a damping term and is treated implicitly, the second is of the opposite sign and 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.

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