Lattice Boltzmann method for groundwater flow in non-orthogonal structured lattices

The efficiency of the lattice Boltzmann method (LBM) in modeling isotropic groundwater flow in domains of arbitrary geometry has been investigated. The Poisson equation was transformed in general curvilinear coordinates. The corresponding equilibrium function for the D2Q9 square lattice based on metric function between the physical and the computational domain has been established. The resulting LBM was checked on examples having higher generality; flows in confined and unconfined aquifers, in vertical and horizontal plane have been considered. In addition, the phreatic water table representing upper boundary in the vertical plane was determined by the dynamic σσ-stretching approach, not requiring complex concepts for dealing with the free surface (like the volume of fluid method). The accuracy and stability of the model is controlled by the adaptive mesh concept. This allows application of higher density grid in critical areas with high pressure and velocity gradients, and vice versa. The number of computation points is significantly reduced without loosing accuracy. The basic characteristics of the LBM including features like parallelization and simplicity, are maintained. The advantages of the proposed curvilinear LBM in modeling groundwater flow in domains of complex shape over the former published methods is demonstrated by three examples.