Multiple-time-scaling lattice Boltzmann method for the convection diffusion equation.

Abstract

A multiple-time-scaling (MTS) strategy that decouples the time discretization in different domains and enables flexible time-step coarsening, refinement, and stretching in the lattice Boltzmann method (LBM) for the convection diffusion equation is developed. The key in the multiple-time scaling is the satisfaction of physical interface conditions without nested iterations in each time step by implementing appropriate interface schemes for the distribution functions in the LBM. The applicability and second-order accuracy of the MTS-LBM approach is demonstrated with two numerical tests. Our approach greatly expands the avenue and expedites the progress of applying the LBM for modeling complex flows and transport phenomena involving multiphases and multicomponents with large property ratios.