Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes

Mark H. Carpenter, David Gottlieb, Saul Abarbanel

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533 Scopus citations

Abstract

We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Padé-like) high-order finite-difference schemes for hyperbolic systems. First a proper summation-by-parts formula is found for the approximate derivative, A “simultaneous approximation term” is then introduced to treat the boundary conditions. This procedure leads to timestable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach.

Original languageEnglish
Pages (from-to)220-236
Number of pages17
JournalJournal of Computational Physics
Volume111
Issue number2
DOIs
StatePublished - Apr 1994
Externally publishedYes

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