On conservation and stability properties for summation-by-parts schemes

Jan Nordström, Andrea A. Ruggiu

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

We discuss conservative and stable numerical approximations in summation-by-parts form for linear hyperbolic problems with variable coefficients. An extended setting, where the boundary or interface may or may not be included in the grid, is considered. We prove that conservative and stable formulations for variable coefficient problems require a boundary and interface conforming grid and exact numerical mimicking of integration-by-parts. Finally, we comment on how the conclusions from the linear analysis carry over to the nonlinear setting.

Original languageEnglish
Pages (from-to)451-464
Number of pages14
JournalJournal of Computational Physics
Volume344
DOIs
Publication statusPublished - 1 Sept 2017
Externally publishedYes

Keywords

  • Boundary conditions
  • Conservation
  • Hyperbolic problems
  • Interface conditions
  • Stability
  • Summation-by-parts

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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