Author(s)

Lei Zhang¹, Jun Yao^1*, Hai Sun^1,2, Jianguang Zhang¹

¹School of Petroleum Engineering, China University of Petroleum, Qingdao, China.
²School of Geosciences, China University of Petroleum, Qingdao, China.

The calculation sequence of collision, propagation and macroscopic variables is not very clear in lattice Boltzmann method (LBM) code implementation. According to the definition, three steps should be computed on all nodes respectively, which mean three loops are needed. While the “pull” scheme makes the only one loop possible for coding, this is called semi-implicit scheme in this study. The accuracy and efficiency of semi-implicit scheme are discussed in detail through the simulation of lid-driven cavity flow. Non-equilibrium extrapolation scheme is adopted on the boundary of simulation area. The results are compared with two classic articles, which show that semi-implicit scheme has good agreement with the classic scheme. When Re is less than 3000, the iterations steps of semi-scheme can be decreased by about 30% though comparing the semi-implicit scheme with standard scheme containing three loops. As the Re increases into more than 3400, the standard scheme is not converged. On the contrary, the iterations of semi-implicit scheme are approximately linear to Re.

Lattice Boltzmann, Cavity Flow, Reynolds Number, Semi-Implicit

Zhang, L. , Yao, J. , Sun, H. and Zhang, J. (2015) A Semi-Implicit Scheme of Lattice Boltzmann Method for Two Dimensional Cavity Flow Simulation. Open Journal of Fluid Dynamics, 5, 10-16. doi: 10.4236/ojfd.2015.51002.