无限长尖端滞止区圆柱绕流无粘分离流的差分算法
Finite-Difference Implementation of Inviscid Separated Flows with Infinitely-Long Cusp-Ended Stagnation Zone around Circular Cylinder
摘要：
本文应用经典的Helmholtz问题对圆柱尖端无粘分离流进行了建模和数值研究。采用两种坐标系：极坐标系用于初始计算，抛物线坐标系作为拓扑学上最适合于无穷大滞止区的坐标系。通过未知自由线的形状进行缩放，将问题呈现为具有固定边界的计算域。给出了Laplace方程和Bernoulli积分的差分格式和算法。获得了阻力系数为$C_x=0$的分离流，类似于所谓的"临界"流。圆柱表面和分离点上的压力分布与速度图法的预测值在定量上进行了很好的比较。
英文摘要：
The classical Helmholtz problem is applied for modelling and numerical investigation of inviscid cusp-ended separated flow around circular cylinder. Two coordinate systems are used: polar for initial calculations and parabolic as topologically most suited for infinite stagnation zone. Scaling by the shape of the unknown free line renders the problem to computational domain with fixed boundaries. Difference schemes and algorithm for Laplace equation and for Bernoulli integral are devised. A separated flow with drag coefficient $C_x=0$ like the so called ``critical'' flow is obtained. The pressure distribution on the surface of cylinder and the detachment point compares quantitatively very well with the predictions of the hodograph method.
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