A New Diffusing-Vortex Numerical Scheme

将求解二维不可压缩Navier-Stokes方程的扩散涡方法推广到一般光滑钝体上的外不可压缩粘性流动。与其他朗朗日涡旋方法相比，该方法的数值优势将通过减少总CPU时间和避免截止程序进一步证明。该方法是扩散方程格林函数的近似表达式，适用于一般二维高雷诺数光滑轮廓。本文将以圆柱问题为例，检验代码的准确性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旋方法的有限差分分析方法可以应用于非定常不可压缩黏性流动，这种非定常不可压缩黏性流动通过典型的圆形、椭圆形和其他类型的圆柱体，其CPU时间比涡旋方法少一个数量级。

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.