Modeling groundwater flow by lattice Boltzmann method in curvilinear coordinates

In order to promote the use of the lattice Boltzmann method (LBM) for the simulation of isotropic groundwater flow in a confined aquifer with arbitrary geometry, Poisson's equation was transformed into a curvilinear coordinate system. With the metric function between the physical and the computational domain established, Poisson's equation written in Cartesian coordinates was transformed in curvilinear coordinates. Following, the appropriate equilibrium function for the D2Q9 square lattice has been defined. The resulting curvilinear formulation of the LBM for groundwater flow is capable of modeling flow in domains of complex geometry with the opportunity of local refining/coarsening of the computational mesh corresponding to the complexity of the flow pattern and the required accuracy. Since the proposed form of the LBM uses the transformed equation of flow implemented in the equilibrium function, finding a solution does not require supplementary procedures along the curvilinear boundaries, nor in the zones requiring mesh density adjustments. Thus, the basic concept of the LBM is completely maintained. The improvement of the proposed LBM over the previously published classical methods is completely verified by three examples with analytical solutions. The results demonstrate the advantages of the proposed curvilinear LBM in modeling groundwater flow in complex flow domains.