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

Highlights: • We have proposed a mesh-free lattice Boltzmann numerical method. • The method collects the advantages of the lattice Boltzmann method and mesh-free methods. • Our method shows superior performance over the standard lattice Boltzmann method in the simulation of geometrically complex flows. - Abstract: 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.