Enhancing the convergence speed of numerical solution using the flow rate control in a novel lattice Boltzmann method

Abstract

In this paper, the lattice Boltzmann method (LBM) is modified using a flow rate control code to enhance the convergence speed and decrease the solution time. The mass flow rate is checked at each cross section for the modified lattice Boltzmann method, while for the regular lattice Boltzmann method, the mass flow rate only is checked at the outlet section of the channel. The results obtained by the modified lattice Boltzmann method are compared with the regular lattice Boltzmann one and finite volume methods for different types of channel flow including simple channel, blocked channel with one and two obstacles, channel with two branching outlets, and curved channel with 90-degree bend. The effects of Reynolds number, under relaxation factor, and mesh number on the iteration number and solution time are studied. The results showed that the solution time of a simple channel decreases about 87%, 77%, and 63% for mesh numbers $ 40\times 400$ , $ 60 \times 600$ , and $ 80 \times 800$ , respectively using the modified LBM as compared with the regular one at under relaxation factor of 0.4 and $ {\rm Re}=100$ . For a blocked channel with one obstacle, the iteration number decreases about 10 times by using the modified LBM as compared with the regular one for a mesh size of $ 40\times 400$ . Finally, the modified LBM enhances the speed of the solution about 57%, 40%, and 73% for the channel with 90-degree bend, the channel with two branching outlets, and blocked channel with two obstacles, respectively, as compared with the regular LBM.