On time relaxed schemes and formulations for dispersive wave equations

Jean Paul Chehab, Denys Dutykh

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The numerical simulation of nonlinear dispersive waves is a central research topic of many investigations in the nonlinear wave community. Simple and robust solvers are needed for numerical studies of water waves as well. The main difficulties arise in the numerical approximation of high order derivatives and in severe stability restrictions on the time step, when explicit schemes are used. In this study we propose new relaxed system formulations which approximate the initial dispersive wave equation. However, the resulting relaxed system involves first order derivatives only and it is written in the form of an evolution problem. Thus, many standard methods can be applied to solve the relaxed problem numerically. In this article we illustrate the application of the new relaxed scheme on the classical Korteweg-de Vries equation as a prototype of stiff dispersive PDEs.

Original languageBritish English
Pages (from-to)254-278
Number of pages25
JournalAIMS Mathematics
Volume4
Issue number2
DOIs
StatePublished - 2019

Keywords

  • Dispersive wave equations
  • Quasi-compressibility
  • Relaxation
  • Shallow water flows

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