Regional scale transient groundwater flow modeling using Lattice Boltzmann methods

Lattice Boltzmann (LB) models can be used to simulate flow in porous media at scales much larger than pore size. LB-based models for such macroscopic scale porous media flow simulations are an extension of standard LB models. There are at least two alternative approaches for implementing such models. In the first approach the local velocity is altered during the collision step by incorporating an external force, F, equivalent to the damping effect of solid particles in porous media. The porous media can be permeable or impermeable depending upon the external forcing term. A sink term is introduced in the LB model to simulate a pumping well and this model is further applied to solve transient ground water well problems for confined aquifers. Directly solving the ground water flow equation with an LB model by exploiting its ability to solve the diffusion equation is another strategy. The second order transient ground water flow equation is analogous to the diffusion equation and mass diffusivity is analogous to hydraulic diffusivity. This diffusion model is used to solve transient ground water problems. Simulated results accurately match analytical solutions of the transient ground water flow equation.