Comparison of Lattice Boltzmann and Finite Difference Methods in the Solution of Coupled Groundwater and Contaminant Transport Equations

Lattice Boltzmann method is a powerful numerical method for the simulation of fluid flow. There are two approaches for the description of groundwater flow in porous media. In the first approach, Navier-Stokes equations are used, while diffusion equation is applied to describe groundwater flow in the second approach. In this research, groundwater flow is modeled using the second approach. Furthermore, the governing equation of contaminant transport is called advection-dispersion equation. Here for the first time, the coupled solution of groundwater flow and contaminant transport using Lattice Boltzmann method is performed. The results indicated that Lattice Boltzmann method is capable of solving groundwater and contaminant transport equations simultaneously with high precision. Moreover, it was found that although the accuracy of Lattice Boltzmann and Crank-Nicolson method are the same, the speed of Lattice Boltzmann method is much higher than finite difference methods. In addition, Lattice Boltzmann method has higher range of stability and consistency in comparison with explicit finite difference method. Regarding this issue, grid Peclet number smaller than 7 is recommended for D1Q2 scheme of LBM.