Scale-selective Time Integration for Long-Wave Linear Acoustics

Stefan Vater*, Rupert Klein, Omar M. Knio

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this note, we present a new method for the numerical integration of one dimensional linear acoustics with long time steps. It is based on a scale-wise decomposition of the data using standard multigrid ideas and a scale-dependent blending of basic time integrators with different principal features. This enables us to accurately compute balanced solutions with slowly varying short-wave source terms. At the same time, the method effectively filters freely propagating compressible short-wave modes. The selection of the basic time integrators is guided by their discrete-dispersion relation. Furthermore, the ability of the schemes to reproduce balanced solutions is shortly investigated. The method is meant to be used in semi-implicit finite volume methods for weakly compressible flows.

Original languageEnglish (US)
Pages (from-to)771-779
Number of pages9
JournalSpringer Proceedings in Mathematics
StatePublished - 2011
Externally publishedYes


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

ASJC Scopus subject areas

  • General Mathematics
  • Statistics, Probability and Uncertainty


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