高阶紧致格式求解二维粘性不可压缩复杂流场

SOLVING TWO DIMENSIONAL INCOMPRESSIBLE VISCOUS COMPLEX FLOW WITH HIGH ORDER COMPACT SCHEME

提出了一种求解二维不可压缩复杂流场的高精度算法．控制方程为原始变量、压力Ｐｏｉｓｓｏｎ方程提法．在任意曲线坐标下，采用四阶紧致格式求解Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程组，时间推进采用交替方向隐式（ＡＤＩ）格式，在非交错网格上用松弛法求解压力Ｐｏｉｓｓｏｎ方程．对于复杂的流场，采用了区域分解方法，并在每一时间步对各子域实施松弛迭代使之能精确地反映非定常流场．利用该算法计算了二维受驱空腔流动，弯管流动和垂直平板的突然起动问题．计算结果与实验结果和其他研究者的计算结果相比较吻合良好．对于平板起动流动。

The paper presents a high accurate method for two dimensional incompressible viscous complex flow. Governing equations are used to adopt primitive variables and the formulation of Poisson equation for pressure. The Navier Stokes equation is solved by fourth order accurate compact scheme making as block tridiagonal linear equations for space and the ADI method for time advance in the general non staggered grid system, and the SOR method solves Poisson equation of pressure. A domain decomposition method is used for complex flow field to improve and to predict the feature and charact er of unsteady flow, by a sub iterative procedure with a successes relaxation scheme for every overlapping sub domain in each time step. The shear driven cavity flow, flow passing the curved tube and unsteady flow past a flat plate normal to the direction of motion have been calculated by this method. The results compare agree well with the experiment and some calculating results reported by other authors.