A numerical scheme with a mesh on characteristics for the cauchy problem for one-dimensional hyperbolic conservation laws

Daeki Yoon, Hongjoong Kim, Woonjae Hwang

Research output: Contribution to journalArticle

Abstract

In this paper, a numerical scheme is introduced to solve the Cauchy problem for one-dimensional hyperbolic equations. The mesh points of the proposed scheme are distributed along characteristics so that the solution on the stencil can be easily and accurately computed. This is very important in reducing errors of the scheme because many numerical errors are generated when the solution is estimated over grid points. In addition, when characteristics intersect, the proposed scheme combines corresponding grid points into one and assigns new characteristic to the point in order to improve computational efficiency. Numerical experiments on the inviscid Burgers' equation have been presented.

Original languageEnglish
Pages (from-to)459-466
Number of pages8
JournalCommunications of the Korean Mathematical Society
Volume24
Issue number3
DOIs
Publication statusPublished - 2009 Dec 1

Keywords

  • Conservation laws
  • Moving mesh
  • Non-oscillatory scheme

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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