Least-squares-based lattice Boltzmann method: A meshless approach for simulation of flows with complex geometry - art. no. 045701

A version of lattice Boltzmann method (LBM) is presented in this work, whic h is derived from the standard LBM by using Taylor series expansion and opt imized by the least squares method. The method is basically meshless, and c an be applied to any complex geometry and nonuniform grids. It can also be applied to different lattice models. The proposed method explicitly updates the distribution functions at mesh points by an algebraic formulation, in which the relevant coefficients are precomputed from the coordinates of mes h points. We have successfully applied this method to simulate many two-dim ensional incompressible viscous flows. The numerical results are very accur ate, and the computational time needed is much less as compared with other existing methods. In this paper, we mainly show the method.