A scale-selective multilevel method for long-wave linear acoustics

Stefan Vater*, Rupert Klein, Omar M. Knio

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


A new method for the numerical integration of the equations for one-dimensional linear acoustics with large time steps is presented. While it is capable of computing the "slaved" dynamics of short-wave solution components induced by slow forcing, it eliminates freely propagating compressible short-wave modes, which are under-resolved in time. Scale-wise decomposition of the data based on geometric multigrid ideas enables a scale-dependent blending of time integrators with different principal features. To guide the selection of these integrators, the discrete-dispersion relations of some standard second-order schemes are analyzed, and their response to high wave number low frequency source terms are discussed. The performance of the new method is illustrated on a test case with "multiscale" initial data and a problem with a slowly varying high wave number source term.

Original languageEnglish (US)
Pages (from-to)1076-1108
Number of pages33
JournalActa Geophysica
Issue number6
StatePublished - Dec 2011
Externally publishedYes


  • balanced modes
  • implicit time discretization
  • large time steps
  • linear acoustics
  • multiscale time integration

ASJC Scopus subject areas

  • Geophysics


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