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 Di erence (FD) solutions, including Explicit Finite Di erence (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 arti cial 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.

Understanding the effects of subsidence on unconfined aquifer parameters by integration of Lattice Boltzmann Method (LBM) and Genetic Algorithm (GA)

“…The first application of the LBM was implemented by Gladrow (Gladrow 1994) who proposed Lattice Boltzmann equation (LBE) models for diffusion instead of lattice gas automata due to its greater flexibility and freedom. The LBM has been successful performance in fluid flow modelling such as Navier-Stokes (Ansumali et al 2007), shallow water [Liu et al 2013, Peng et al 2011, Zhou 2004, groundwater (Zhou 2007a;Zhou 2011;Budinski et al 2015;Arsyad et al 2017;Hekmatzadeh et al 2018;, and especially multiphase flow in porous media [Anwar and Sukop 2008;Fattahi et al 2016;Gharibi and Ashrafizaadeh 2020). LBM has been widely applied to explore heat and mass transfer problems such as pollutant transport (Lei et al 2013), thermal response (Gao et al 2021), saltwater intrusion (Servan-Camas and T.-C. Tsai 2009) and reaction diffusion (Lin et al 2021).…”

The solution of unconfined groundwater flow with an innovative lattice Boltzmann method

“…Moreover, the LB methods benefit from fast computational ability and admirable stability, especially in time-dependent problems. This method shows superior capability to meet with parallel programming techniques utilizing graphics processing unit (GPU) [2,3]. This method has various applications in the simulation of different physical phenomena such as solitary wave [4], convection-diffusion equations [5], shallow water [6], heat conduction [7], and kinetic equations [8].…”

“…The diffusion equation governs groundwater flow, while advection-diffusion equation describes the solute transport [2,9,10]. It is worth noting that various lattice configurations have been developed for LBM to solve mass transfer equations, containing D1Q2 and D1Q3 for one dimensional problems, D2Q4, D2D5, and D2Q9 for two dimensional problems, in addition to, D3Q15 and D3Q19 for the three dimensions [3,[11][12][13].…”