Lattice Boltzmann method for 3-D flows with curved boundary

In this work, we investigate two issues that are important to computational efficiency and reliability in fluid dynamic applications of the lattice Bo ltzmann equation (LBE): (1) Computational stability and accuracy of differe nt lattice Boltzmann models and (2) the treatment of the boundary condition s on curved solid boundaries and their 3-D implementations. Three athermal 3-D LEE models (Q15D3, Q19D3, and 427D3) are studied and compared in terms of efficiency, accuracy and robustness. The boundary treatment recently dev eloped by Filippova and Hanel (1998, J. Comp. Phys. 1.47, 219) and Mei et a l. (1999, J. Comp. Phys. 155, 307) in 2-D is extended to and implemented fo r 3-D. The convergence, stability, and computational efficiency of the 3-D LEE models with the boundary treatment for curved boundaries were tested in simulations of four 3-D flows: (1) Fully developed flows in a square duct, (2) flow in a 3-D lid-driven cavity, (3) fully developed flows in a circul ar pipe, and (4) a uniform flow over a sphere. We found that while the 15-v elocity 3-D (Q15D3) model is more prone to numerical instability and the Q2 7D3 is more computationally intensive, the Q19D3 model provides a balance b etween computational reliability and efficiency. Through numerical simulati ons, we demonstrated that the boundary treatment for 3-D arbitrary curved g eometry has second-order accuracy and possesses satisfactory stability char acteristics. (C) 2000 Academic Press.