基于时间的驱动方腔流的高精度多重网格方法数值模拟

NUMERICAL SIMULATION OF TIME-DEPENDENT DRIVEN CAVITY FLOW WITH HIGH ACCURACY MULTIGRID METHOD

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 compact fourth-order finite difference with a second-order fully implicit time-marching scheme is proposed to solve the two-dimensional unsteady incompressible Navier-Stokes equations. A multigrid full approximation scheme(FAS) is applied to accelerate convergence for the implicit scheme at each time step. The numerical results for driven cavity flow show good agreement with the results in literature not only for steady laminar solution when Re≤5000 on coarse meshes (e.g. 64×64. or. 128×128)but for unsteady periodic solution when Re = 7500 and Re = 10000 on 256×256 meshes for the appearance of more secondary vortices in the flow field.