A computational strategy for multiscale systems with applications to Lorenz 96 model

Ibrahim Fatkullin, Eric Vanden-Eijnden

Research output: Contribution to journalArticle

63 Scopus citations

Abstract

Numerical schemes for systems with multiple spatio-temporal scales are investigated. The multiscale schemes use asymptotic results for this type of systems which guarantee the existence of an effective dynamics for some suitably defined modes varying slowly on the largest scales. The multiscale schemes are analyzed in general, then illustrated on a specific example of a moderately large deterministic system displaying chaotic behavior due to Lorenz. Issues like consistency, accuracy, and efficiency are discussed in detail. The role of possible hidden slow variables as well as additional effects arising on the diffusive time-scale are also investigated. As a byproduct we obtain a rather complete characterization of the effective dynamics in Lorenz model.

Original languageEnglish (US)
Pages (from-to)605-638
Number of pages34
JournalJournal of Computational Physics
Volume200
Issue number2
DOIs
StatePublished - Nov 1 2004
Externally publishedYes

Keywords

  • Averaging techniques
  • Effective dynamics
  • Heterogeneous Multiscale Method (HMM)
  • Lorenz 96 model
  • Mode reduction
  • Multiscale numerical methods

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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