In this study, we utilize the lattice Boltzmann method to investigate the flow behavior in a two-dimensional trapezoidal cavity, which is driven by both sides on the upper wall and lower wall. Our calculations are accelerated through GPU-CUDA software. We conduct an analysis of the flow field mode by 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 are shown below. 1) For the upper wall drive (T1a), the flow field remains stable, when the Re value varies from 1000 to 8000. However, when Re = 8500, the flow field becomes periodic but unstable. The velocity phase diagram at the monitoring point is a smooth circle, and the energy values of the first two modes dominate 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) For the lower wall drive (T1b), the flow is stable when Re value is in a range of 1000－8000, and it becomes periodic and unsteady when Re = 11500. The energy values of the first three modes appear 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 values of the first two modes almost entirely dominating the entire energy. 3) For the case of upper wall and lower wall moving in the same direction at the same speed (T2a), the flow field remains stable when Re changes from 1000 to 10000. When Re varies from 12500 to 15000, the flow becomes periodic and unstable. The velocity phase diagram is still a smooth circle, with the first two modes still occupying a large portion of the energy. Once Re exceeds 20000, the energy proportions of the first three modes significantly decrease, and the flow becomes aperiodic and unsteady. 4) For the case in which the upper wall and lower wall are driven in opposite directions at the same velocity (T2b), the flow field remains stable when Re changes from 1000 to 5000. When Re = 6000, the energy of the first mode accounts for 86%, and the flow field becomes periodic but unstable. When Re exceeds 8000, the energy proportions of the first three modes decrease significantly, and the flow field becomes aperiodic and unsteady.