Lattice Boltzmann solution of advection-dominated mass transport problem: A comparison

Abstract

This article addresses the abilities and limitations of the Lattice Boltzmann (LB) method in solving advection-dominated mass transport problems. Several schemes of the LB method, including D2Q4, D2Q5, and D2Q9, were assessed in the simulation of two-dimensional advection-dispersion equations. The concepts of Single Relaxation Time (SRT), Multiple Relaxation Time (MRT), and linear and quadratic Equilibrium Distribution Functions (EDF) were taken into account. The results of LB models were compared to the well-known Finite Difference (FD) solutions, including Explicit Finite Difference (EFD) and Crank-Nicolson (CN) methods. All LB models are more accurate than the aforementioned FD schemes. The results also indicate the high potency of D2Q5 SRT and D2Q9 SRT in describing advection-controlled mass transfer problems. The numerical artificial oscillations are observed when the Grid Peclet Number (GPN) is greater than 10, 25, 20, 25, and 10 regarding D2Q4 SRT, D2Q5 SRT, D2Q5 MRT, D2Q9 SRT, and D2Q9 MRT, respectively, while the corresponding GPN values obtained for the EFD and CN methods were 2 and 5, respectively. Finally, several LB models were used to satisfactorily solve a coupled system of groundwater and solute transport equations. In terms of computational time, all LB models are much faster than CN method.