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提出了一种求解二维非定常不可压缩Navier-Stokes方程组的全隐二阶时间推进和空间四阶差分紧致格式,在每一个时间步上,采用多重网格的全近似格式(FAS)加速其迭代收敛过程。利用该方法对驱动方腔流动问题进行了直接数值模拟,结果显示对于Re≤5000,本文在粗网格上(64×64等分和128×128等分)即可得到较为准确的定常层流解;对于Re=7500和10000,由于更多二次涡的出现,本文在256×256等分网格上同样可得到与前人的结果相吻合的非定常周期性解。
A total implicit second-order time-based solution and a fourth-order difference compactly format for solving a two-dimensional unsteady incompressible Navier-Stokes equations are proposed. At each time step, the full approximation format of multiple grids (FAS) Accelerate its iterative convergence process. This method is used to directly simulate the flow in the driving cavity. The results show that for Re≤5000, a more accurate steady-state laminar flow can be obtained on the coarse grid (64 × 64 and 128 × 128) For Re = 7500 and 10000, due to the appearance of more secondary vortexes, we also obtain the unsteady periodic solutions that are consistent with the previous results on a 256 × 256 grid.