Lattice Boltzmann simulation and analysis of two-dimensional trapezoidal cavity flow based on GPU

Abstract

In this study, we utilize the lattice Boltzmann method to investigate the flow behavior in a two-dimensional trapezoidal cavity, which is under two-sided driving on the upper and lower walls. Our calculations have been accelerated through GPU-CUDA software. We have conducted an analysis of the flow field mode using proper orthogonal decomposition. The effects of various parameters such as Reynolds number (Re) and driving direction on the flow characteristics are examined through numerical simulations. The results show that:(1) for the upper wall drive (T1a), the flow field remains stable within the range of Re from 1000 to 8000. However, when Re=8500, the flow field becomes periodic yet unstable. The velocity phase diagram at the monitoring point is a smooth circle, and the energy of the first two modes has dominated the energy of the whole field. Once Re exceeds 10000, the velocity phase diagram turns irregular and the flow field becomes aperiodic and unsteady. (2) As for the lower wall drive (T1b), the flow is stable within Re 1000-8000, yet when Re=11500, the flow field becomes periodic yet unsteady. The energy of the first three modes appears relatively large. When Re is greater than 12500, the flow field becomes aperiodic and unsteady. At this time, the phase diagram exhibits a smooth circle, with the energy of the first two modes almost entirely dominating the entire energy. (3) For the case of upper and lower walls moving in the same direction with the same speed (T2a), the flow field remains stable when Re changes from 1000 to 10000. When Re is between 12500 to 15000, the flow becomes periodic yet unstable. The velocity phase diagram continues to be a smooth circle, with the first two modes still occupying a large portion of the energy. Once Re surpasses 20000, the energy proportion of the first three modes significantly decreases, and the flow becomes aperiodic and unsteady. (4) For the case in which the upper and lower walls are driven in opposite directions with the same velocity (T2b), the flow field remains stable within Re changes from 1000 to 5000. When Re=6000, the energy of the first mode accounts for 86%, and the flow field becomes periodic yet unstable. When Re surpasses 8000, the energy proportion of the first three modes decreases significantly, and the flow field becomes aperiodic and unsteady.