A lattice Boltzmann method (LBM) based on nonuniform quadtree mesh is proposed. For the two steps in LBM, the collision step is a local procedure and can be implemented in the same way for both uniform and nonuniform mesh grids, while the streaming step is equivalent to solving several linear advection equations. On quadtree mesh (and some other nonuniform meshes), it is usually trivial to construct a first order interpolation scheme for the streaming step. Then the back and forth error compensation and correction (BFECC) method is employed to improve the accuracy order, such that a second order scheme is obtained in streaming step. Several numerical test cases are carried out to prove the accuracy and efficiency of our method.
Rapid gravity gradiometry terrain correction via adaptive quadtree mesh discretization
