An approach to determine the solid volume fraction near solid boundaries for partially saturated method within the lattice Boltzmann method

Within the LBM (Lattice Boltzmann Method), PSM (Partially Saturated Method) is a quite straightforward approach for dealing with solid boundaries. Additionally, PSM also has the advantages of mass-conserving and no fresh node problem. There have been numerous successful implementations of PSM in processing the fluidsolid interactions in previous investigations. In PSM, calculating the solid volume fraction in cubic LBM cells near solid boundaries is an indispensable prerequisite. However, the methods adopted in the previous work have quite low efficiency in determining the solid fraction for complex boundaries. Additionally, most of the PSM-LBM investigations concentrate on the boundary with rather simple geometry (e.g., the sphere in 3D and the circle in 2D). Therefore, an approach based on the projection method is proposed in this paper to accurately and efficiently determine the solid volume fraction of complex boundaries in a cubic cell. To demonstrate the capability of our proposed approach, the calculation results of the solid volume fraction are compared with the theoretical solution of a spherical solid and the subdivision method. The comparison results demonstrate that this approach is up to 10 times more efficient than the subdivision method for the same level of accuracy. Subsequently, the proposed approach is incorporated into PSM-LBM to simulate the flow over a stationary obstacle with a relatively regular shape (including sphere, cube, and ellipsoid) and the quite complex geometry (the rearview mirror) for further verifying the ability of the proposed approach. The fairly favorable consistency between the current simulation results and the literature data can ulteriorly validate the feasibility of this approach in processing fluid-solid interaction involving complex boundaries.