Energy stable and high-order-accurate finite difference methods on staggered grids

Ossian O'Reilly, Tomas Lundquist, Eric M. Dunham, Jan Nordström

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)


For wave propagation over distances of many wavelengths, high-order finite difference methods on staggered grids are widely used due to their excellent dispersion properties. However, the enforcement of boundary conditions in a stable manner and treatment of interface problems with discontinuous coefficients usually pose many challenges. In this work, we construct a provably stable and high-order-accurate finite difference method on staggered grids that can be applied to a broad class of boundary and interface problems. The staggered grid difference operators are in summation-by-parts form and when combined with a weak enforcement of the boundary conditions, lead to an energy stable method on multiblock grids. The general applicability of the method is demonstrated by simulating an explosive acoustic source, generating waves reflecting against a free surface and material discontinuity.

Original languageEnglish
Pages (from-to)572-589
Number of pages18
JournalJournal of Computational Physics
Publication statusPublished - 1 Oct 2017
Externally publishedYes


  • Energy stability
  • High order finite difference methods
  • Staggered grids
  • Summation-by-parts
  • Wave propagation
  • Weakly enforced boundary conditions

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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