A New Diffusing-Vortex Numerical Scheme

用于求解二维不可压缩纳维-斯托克斯方程的扩散涡流方法将被扩展并应用于一般光滑钝体上的外部不可压缩粘性流。 通过减少总 CPU 时间和避免截止程序，将进一步证明相对于其他朗格朗日涡流方法的数值优势。 新方法是扩散方程格林函数的近似表达式，将为高雷诺数下的一般二维平滑轮廓构建。 作为基准案例，圆柱问题将用于检查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。 所提出的基于扩散涡流法的有限差分分析可以应用于经过圆形、椭圆形和其他类型圆柱体等典型二维几何形状的非定常不可压缩粘性流，其CPU时间比涡流法少一个数量级。

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.