Application of flux limiters to passive scalar advection for the lattice Boltzmann method

Abstract

A new scalar advection algorithm is presented for the lattice Boltzmann (LB) method in which numerical diffusion is reduced by a one-dimensional linear approximation paired with a flux limiter and numerical dispersion is minimized by using fluid flux calculations based on the LB distribution function. The algorithm is designed to be conservative and have low memory requirements. A finite volume method (FVM) based on the LB velocity field is also presented for comparison. We validate with uniform velocity and turbulent flow simulations showing that numerical diffusion error matches FVM results while numerical dispersion is reduced. A performance analysis indicates it is less efficient, but we demonstrate that adjusting the scalar advection time step relative to the fluid time step can improve efficiency with minor effects on accuracy.