Coarse-grained numerical bifurcation analysis of lattice Boltzmann models

P. Van Leemput, K. W.A. Lust, I. G. Kevrekidis

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

In this paper we study the coarse-grained bifurcation analysis approach proposed by I.G. Kevrekidis and collaborators in PNAS [C. Theodoropoulos, Y.H. Qian, I.G. Kevrekidis, "Coarse" stability and bifurcation analysis using time-steppers: a reaction-diffusion example, Proc. Natl. Acad. Sci. 97 (18) (2000) 9840-9843]. We extend the results obtained in that paper for a one-dimensional FitzHugh-Nagumo lattice Boltzmann (LB) model in several ways. First, we extend the coarse-grained time stepper concept to enable the computation of periodic solutions and we use the more versatile Newton-Picard method rather than the Recursive Projection Method (RPM) for the numerical bifurcation analysis. Second, we compare the obtained bifurcation diagram with the bifurcation diagrams of the corresponding macroscopic PDE and of the lattice Boltzmann model. Most importantly, we perform an extensive study of the influence of the lifting or reconstruction step on the minimal successful time step of the coarse-grained time stepper and the accuracy of the results. It is shown experimentally that this time step must often be much larger than the time it takes for the higher-order moments to become slaved by the lowest-order moment, which somewhat contradicts earlier claims.

Original languageEnglish (US)
Pages (from-to)58-76
Number of pages19
JournalPhysica D: Nonlinear Phenomena
Volume210
Issue number1-2
DOIs
StatePublished - Oct 1 2005

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Keywords

  • Coarse-grained modeling
  • Lattice Boltzmann method
  • Newton-Picard method
  • Numerical bifurcation analysis
  • Reaction-diffusion systems

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