Lattice Boltzmann Method for 3-D Flows with Curved Boundary

Abstract

In this work, we investigate two issues that are important to computational efficiency and reliability in fluid dynamic applications of the lattice Boltzmann equation (LBE): (1) Computational stability and accuracy of different 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 (Q15D3, Q19D3, and Q27D3) are studied and compared in terms of efficiency, accuracy, and robustness. The boundary treatment recently developed by Filippova and Hänel (1998, J. Comp. Phys.147, 219) and Mei et al. (1999, J. Comp. Phys.155, 307) in 2-D is extended to and implemented for 3-D. The convergence, stability, and computational efficiency of the 3-D LBE 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 circular pipe, and (4) a uniform flow over a sphere. We found that while the 15-velocity 3-D (Q15D3) model is more prone to numerical instability and the Q27D3 is more computationally intensive, the Q19D3 model provides a balance between computational reliability and efficiency. Through numerical simulations, we demonstrated that the boundary treatment for 3-D arbitrary curved geometry has second-order accuracy and possesses satisfactory stability characteristics.