A rectangular lattice Boltzmann method for groundwater flows

A novel approach is proposed to achieve the solution of the lattice Boltzmann equation on a rectangular mesh without use of any additional numerical scheme unlike an existing method. This is a natural and further development of the author's lattice Boltzmann model for groundwater flows on a square lattice. It solves the isotropic groundwater equation on a rectangular lattice, which enables flow problems characterized by fast variation in one direction and relatively slow in another to be simulated with fine and coarse meshes, respectively, resulting in more efficient algorithm. The stability conditions are also discussed. The method is then verified by solving two benchmark tests for groundwater flows. The numerical predictions are in good agreement with the corresponding exact/analytical solutions. This suggests that the method is simple, accurate and robust for groundwater flows.