Determination of dimensional flow fields in hydrogeological settings via the MRT lattice-Boltzmann method

In this paper we demonstrate how the single and multiple-relaxation-time (MRT) lattice-Boltzmann (LB) method can be used to simulate hydrogeological flows under standard conditions. We explain in detail how real-world hydrogeological flow problems, which are formulated in terms of dimensional boundary and initial conditions, can be related to the nondimensional LB world, in which both the lattice spacing and the time step are nondimensional and typically set to unity. We first demonstrate the method in two examples where analytical solutions are known: steady state and transient flow of water in a square duct where fluid inertia is either negligible or not, respectively. Finally we simulate the flow of water in a sand where inertial forces are not negligible. For steady state flow we also present equations for calculating the permeability. Moreover, we demonstrate and advocate the usage of Richardson's extrapolation, which allows one to estimate LB modeling results for an infinite numerical resolution that include uncertainty intervals. For pressure-driven simulations of steady state creeping flow, we show how one can improve the numerical convergence behavior by performing "light-water" simulations at a lower Reynolds number while still predicting the correct velocity field.