Lattice Boltzmann Method for 3-D Flowswith Curved Boundary

In this work, we investigate two issues that are important to computational e ciency and reliability in uid dynamics applications of the lattice Boltzmann equation (LBE): (1) Computational stability and accuracy of di erent lattice Boltzmann models and (2) the treatment of the boundary conditions on curved solid boundaries and their 3-D implementations. Three athermal 3-D LBE models (D3Q15, D3Q19, and D3Q27) are studied and compared in terms of e ciency, accuracy, and robustness. The boundary treatment recently developed by Filippova and Hanel and Mei et al. in 2-D is extended to and implemented for 3-D. The convergence, stability, and computational e ciency of the 3-D LBE models with the boundary treatment for curved boundaries were tested in simulations of four 3-D ows: (1) Fully developed ows in a square duct, (2) ow in a 3-D lid-driven cavity, (3) fully developed ows in a circular pipe, and (4) a uniform ow over a sphere. We found that while the fteen-velocity 3-D (D3Q15) model is more prone to numerical instability and the D3Q27 is more computationally intensive, the D3Q19 model provides a balance between computational reliability and e ciency. Through numerical simulations, we demonstrated that the boundary treatment for 3-D arbitrary curved geometry has second-order accuracy and possesses satisfactory stability characteristics.