We demonstrate that the asymptotic approximant applied to the Blasius boundary layer flow over a flat plat (Barlow et al., Q. J. Mech. Appl. Math. 70 (2017) 21–48.) yields accurate analytic closed-form solutions to the Falkner–Skan boundary layer equation for flow over a wedge having angle |$\beta\pi/2$| to the horizontal. A wide range of wedge angles satisfying |$\beta\in[-0.198837735, 1]$| are considered, and the previously established non-unique solutions for |$\beta<0$| having positive and negative shear rates along the wedge are accurately represented. The approximant is used to determine the singularities in the complex plane that prescribe the radius of convergence of the power series solution to the Falkner–Skan equation. An attractive feature of the approximant is that it may be constructed quickly by recursion compared with traditional Padé approximants that require a matrix inversion. The accuracy of the approximant is verified by numerical solutions, and benchmark numerical values are obtained that characterize the asymptotic behavior of the Falkner–Skan solution at large distances from the wedge.

中文翻译：

---

Falkner–Skan边界层方程的渐近近似

我们表明，渐近逼近应用于在平板型的布拉休斯边界层流（巴洛等人，QJ机甲。应用数学。 70（2017）21-48。），得到精确的解析封闭形式解Falkner-角为| $ \ beta \ pi / 2 $ |的楔形上流动的Skan边界层方程 到水平。满足| $ \ beta \ in [-0.198837735，1] $ |的各种楔角 被考虑，并且先前为| $ \ beta <0 $ |建立的非唯一解沿楔形具有正和负剪切速率的精确表示。该近似值用于确定复平面中的奇点，该奇点规定了Falkner–Skan方程的幂级数解的收敛半径。该近似值的一个吸引人的特征是，与需要矩阵求逆的传统Padé近似值相比，该近似值可以通过递归快速构建。通过数值解验证了近似值的准确性，并获得了基准数值，这些数值表征了距楔形物很远的Falkner-Skan解的渐近行为。