用分步有限元法求解三维不可压缩流动

将计算二维不可压缩流动的分步有限元格式扩展到三维情况 ,由于该格式没有引入新的高阶空间导数项 ,适用于多维空间的非线性问题。实际求解了三维空腔流 ,在 Re数较低的情况下得到的流态不随时间而变化 ;在高 Re数(Re=40 0 0 )的情况下 ,流态十分复杂并且是非定常的 ,在水平断面具有多个非定常旋涡 ,在垂直于流动方向的立面断面上可以模拟到 TGL涡。本格式的迎风效应是 Taylor展开式的高阶精度项 ,没有人工粘性引入 ,得到的结果可靠性好

Fractional step finite element method for three-dimensional incompressible flows

The two dimensional fractional step finite element scheme was extended to three dimensional cases. The stability and numerical accuracy of the 3D case was analyzed showing that the present fractional step finite element scheme has third order accuracy and an extended stability domain. Three dimensional cavity flows were simulated. For small Reynolds numbers, the results are steady. For large Reynolds numbers (i.e., Re =4000), the results are unsteady and the flows are very complicated. The TGL vortices obtained in the present computation are in good agreement with observations.