Numerical bifurcation analysis of lattice Boltzmann models: A reaction-diffusion example

Abstract

We study two strategies to perform a time stepper based numerical bifurcation analysis of systems modeled by lattice Boltzmann methods, one using the lattice Boltzmann model as the time stepper and the other the coarse-grained time stepper proposed in Kevrekidis et al., CMS 1(4). We show that techniques developed for time stepper based numerical bifurcation analysis of partial differential equations (PDEs) can be used for lattice Boltzmann models as well. The results for both approaches are also compared with an equivalent PDE description. © Springer-Verlag Berlin Heidelberg 2004.