Analysis of the applicability of the lattice Boltzmann method in targeting a chaotic flame front model

Abstract

In this paper, we present utilization of the lattice Boltzmann method (LBM) to analyze spatiotemporal chaotic fields. To this end, the one-dimensional Kuramoto–Sivashinsky equation, which is a proper model for unstable flame front flutter, is rewritten in terms of lattice Boltzmann equation components and is then solved. After accuracy checks, we alter the computational domain size and also the control parameter of the problem, which is representative of the kinematic viscosity in real flows, to capture the symmetry-breaking phenomenon. In the next step, since the method is in fact a one-dimensional explicit mapping for the probability density functions, we adopt the targeting algorithm of chaotic fields using LBM. The results show that the method can be applied to chaotic fields with confidence.