A mesh-free lattice Boltzmann solver for flows in complex geometries

Simulation of geometrically complicated flows in which mesh generators have severe mesh quality-related difficulties or even fail to create a mesh is one of the open problems in computational fluid dynamics. In this study, we have proposed a mesh-free lattice Boltzmann method for the solution of geometrically complex fluid flow problems. The main distinction of our method is to consider the streaming equation as a pure advection equation rather than a perfect shift, so that the physical space discretization becomes independent of the lattice. We discretize the advection equation using the Lax-Wendroff scheme in time and the meshless local Petrov-Galerkin scheme based on radial basis functions in space. We first solve two benchmark problems, namely the Poiseuille flow and the lid-driven cavity flow for the validation of the proposed method, and then simulate fluid flow in a two dimensional granular porous medium. The results show that our method outperforms the conventional lattice Boltzmann method in the simulation of geometrically complicated flows.