A New Diffusing-Vortex Numerical Scheme

将求解二维不可压缩N-S方程的扩散涡方法推广应用于一般光滑钝体上的不可压缩粘性外流。通过减少总的CPU时间和避免截断过程，将进一步证明与其他朗格朗日涡旋方法相比的数值优势。新方法是扩散方程格林函数的近似表示，它将被构造为高雷诺数下的一般二维光滑轮廓。以圆柱问题为基准，考察了程序的精度以及空间网格长度和时间步长对计算结果的影响。本文提出的基于扩散涡方法的有限差分方法可用于二维几何形状的不可压缩非定常粘性绕流，其计算时间比涡旋法少一个数量级。

A diffusing-vortex method, for solving the two-dimensional incompressibl Navier-Stokes equation, will be extended and applied to the external incompressible viscous flow over a generally smooth blunt body. The numerical advantages over other Langrangian vortex methods will be further demonstrated by reducing total CPU time and by avoiding cut-off procedures. The new approach, which is an approximate expression of the Green's function of the diffusion equation, will be constructed for a general two-dimensional smooth contour at a high Reynolds number. A benchmark case, the cylinder problem will be used to examine the accuracy of the code and the effect of spatial mesh length and time step length on computational results. The proposed finite difference analysis based on the diffusing vortex method can be applied to the unsteady imcompressible viscous flow past two dimensional geometry typical of circular, elliptic, and other type of cylinders with CPU time less than vortex method by one order of magnitude.