| mesoscopic method to simulation the macroscale transport phenomenon. Compared with the traditional methods, the LBM has many advantages, such as the simplicity of program, location of computation, natural parallel and can deal easily with the complex boundary problems, which is a strong tool to simulate the complex flows. In recent years, the lattice Boltzmann method has been successfully applied into many hydro-fields, such as turbulence, porous media flow, and multiphase fluid flow, suspend particle flow, magneto hydrodynamics and so on. The benchmark problem of computation fluid dynamics, the"driven cavity flow", is often used to test the numerical methods in terms of their efficiency. Up to now, most available literature focuses on lid-driven cavity flow, such as lid-driven square cavity flow, lid-driven flow in a rectangular cavity and so on, which have simple geometries. However, the literature on lid-driven cavity flow with complex geometry is very little.In this paper, the lattice BGK model proposed by Guo et al. is applied to simulate lid-driven flow in a two-dimensional trapezoidal cavity. Due to the complex boundary of the trapezoidal cavity, here, the boundary treatment scheme proposed by Guo et al. is used to the curved boundary. In our simulations, the Reynolds number (Re) is varied from 100 to 15000. For the isosceles trapezoidal cavity and the right-angled trapezoidal cavity, the effects of Reynolds number and the top angleθon the strength, center position and number of vortex are studied. As the Reynolds number increases, the phenomena appeared in the cavity becomes more and more complex, and the number of the vortex is also increased. We find that the vortex at the bottom breakups into two smaller vortices as the top angleθis increased to a critical value. In addition, we also find that as Re≤7500, the flow is steady, as Re is increased to10000, it becomes periodic, and as Re is further increased to 12500, the flow is chaotic.
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