High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates

Jan Nordström, Mark H. Carpenter

Research output: Contribution to journalArticlepeer-review

132 Citations (Scopus)

Abstract

Boundary and interface conditions are derived for high-order finite difference methods applied to multidimensional linear problems in curvilinear coordinates. Difficulties presented by the combination of multiple dimensions and varying coefficients are analyzed. In particular, problems related to nondiagonal norms, a varying Jacobian, and varying and vanishing wave speeds are considered. The boundary and interface conditions lead to conservative schemes and strict and strong stability provided that certain metric conditions are met.

Original languageEnglish
Pages (from-to)149-174
Number of pages26
JournalJournal of Computational Physics
Volume173
Issue number1
DOIs
Publication statusPublished - 10 Oct 2001
Externally publishedYes

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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