Mass-Conserved Wall Treatment of the Non-Equilibrium Extrapolation Boundary Condition in Lattice Boltzmann Method

In lattice Boltzmann simulations, the widely used non-equilibrium extrapolation method for velocity and pressure boundary conditions can cause a constant mass leakage under certain circumstances, particularly when an external force field is imposed on the fluid domain. The non-equilibrium distribution function at the boundary uses a first-order extrapolation method on the corresponding data of adjacent fluid nodes. In addition, based on this extrapolation method, the macroscopic velocity and density at the boundary nodes are obtained. Therefore, the corresponding equilibrium component of the distribution function can be calculated explicitly. Regarding the no-slip wall boundary condition, we found that the mass leakage primarily results from the extrapolation scheme for the density term in the equilibrium component of the distribution function at the boundary node. In this study, a mass-conserved wall treatment method is developed to correct the existing density term for guaranteeing the conservation of mass. Several benchmark test cases were simulated and compared to prove the justification of the newly developed mass-conserved boundary condition, and the results show a good agreement with those in the existing literature.