A mass conserving boundary condition for the lattice Boltzmann equation method

In lattice Boltzmann (LB) simulations, the widely used wall boundary conditions (BCs) proposed by Filipova and Hنnel (FH) and Mei, Luo and Shyy (MLS) result in constant mass leakage in certain circumstances. In this paper, we have analyzed the source of the leakage. Based on this analysis, we propose a second-order accurate mass conserving wall BC. In our BC, the distribution function at a wall node is decomposed into its equilibrium and non-equilibrium parts. The mass conservation is guaranteed by enforcing a mass conserving rule in the construction of the fictitious equilibrium distribution part. We have shown through several benchmark test problems involving steady and unsteady flows that our new BC not only eliminates the constant mass leakage, but also has many other advantages over the FH and MLS BCs.