SBP–SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids

Longfei Gao*, David C. Del Rey Fernández, Mark Carpenter, David Keyes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

Abstract

We consider the numerical simulation of the acoustic wave equations arising from seismic applications, for which staggered grid finite difference methods are popular choices due to their simplicity and efficiency. We relax the uniform grid restriction on finite difference methods and allow the grids to be block-wise uniform with nonconforming interfaces. In doing so, variations in the wave speeds of the subterranean media can be accounted for more efficiently. Staggered grid finite difference operators satisfying the summation-by-parts (SBP) property are devised to approximate the spatial derivatives appearing in the acoustic wave equation. These operators are applied within each block independently. The coupling between blocks is achieved through simultaneous approximation terms (SATs), which impose the interface conditions weakly, i.e., by penalty. Ratio of the grid spacing of neighboring blocks is allowed to be rational number, for which specially designed interpolation formulas are presented. These interpolation formulas constitute key pieces of the simultaneous approximation terms. The overall discretization is shown to be energy-conserving and examined on test cases of both theoretical and practical interests, delivering accurate and stable simulation results.

Original languageEnglish (US)
Pages (from-to)421-444
Number of pages24
JournalJournal of Computational and Applied Mathematics
Volume348
DOIs
StatePublished - Mar 1 2019

Bibliographical note

Publisher Copyright:
© 2018 Elsevier B.V.

Keywords

  • Long time instability
  • Nonconforming interface
  • Seismic wave modeling
  • Simultaneous approximation terms
  • Staggered grid
  • Summation by parts

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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