Review of summation-by-parts schemes for initial-boundary-value problems

Magnus Svärd, Jan Nordström

Research output: Contribution to journalArticlepeer-review

323 Citations (Scopus)

Abstract

High-order finite difference methods are efficient, easy to program, scale well in multiple dimensions and can be modified locally for various reasons (such as shock treatment for example). The main drawback has been the complicated and sometimes even mysterious stability treatment at boundaries and interfaces required for a stable scheme. The research on summation-by-parts operators and weak boundary conditions during the last 20 years has removed this drawback and now reached a mature state. It is now possible to construct stable and high order accurate multi-block finite difference schemes in a systematic building-block-like manner. In this paper we will review this development, point out the main contributions and speculate about the next lines of research in this area.

Original languageEnglish
Pages (from-to)17-38
Number of pages22
JournalJournal of Computational Physics
Volume268
DOIs
Publication statusPublished - 1 Jul 2014
Externally publishedYes

Keywords

  • Simultaneous Approximation Terms
  • Summation-by-Parts schemes

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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