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TW 444
Pieter Van Leemput, Wim Vanroose, and Dirk Roose
Initialization of a lattice Boltzmann model with constrained runs
Abstract
In this article, we perform a numerical stability and convergence analysis of the constrained runs initialization scheme for a lattice Boltzmann model. Gear and Kevrekidis developed this scheme in the context of coarse-grained equation-free computing. Given the macroscopic initial fields, we study the mapping of these variables to the higherdimensional space of lattice Boltzmann variables. The lattice Boltzmann model considered is the BGK collision model for one-dimensional reaction-dision systems. For such systems, we prove that the constrained runs scheme is unconditionally stable and that it converges to an approximation of the slaved state, i.e. the microscopic state consistent with the macroscopic initial condition. This approximation is correct up to first order in the Chapman-Enskog expansion of the lattice Boltzmann model. The asymptotic convergence factor is |1-ω| with ω the BGK relaxation parameter. The results are illustrated for the one-dimensional FitzHugh-Nagumo reaction-dision system. Using the constrained runs initialization in the context of equation-free computing, we also perform a coarsegrained bifurcation analysis of this model.
report.pdf (358K) (revised April 2006) / mailto: P. Van Leemput