Falkner-Skan边界层的相似与伪相似解
On similarity and pseudo-similarity solutions of Falkner-Skan boundary layers
AI总结：
本文研究二维不可压缩层流稳态边界层方程，确定外部速度分布使得问题存在相似解，并详细分析外部速度与距离成反比（U_e(x)=U_∞x^{-1}）时的伪相似新精确解，发现仅在有侧向吸力时存在解，且解的数量无限，包括单调解和无限振荡趋于极限的解，性质依赖于吸力参数，并通过四阶龙格-库塔法和打靶法获得数值解。
摘要：
本文研究二维不可压缩、层流、稳态边界层方程。首先，我们确定边界层外速度分布族，使得这些问题可能存在相似解。然后，我们详细考察新的精确解，称为伪相似解，其中外部速度沿表面x方向与距离成反比变化（U_e(x)=U_∞x^{-1}）。分析表明，解仅存在于有侧向吸力的情况下。这里假设流动由具有拉伸速度U_wx^{-1}的连续渗透表面诱导。在特定条件下，我们建立了无限多个解的存在性，包括单调解和无限次振荡并趋于某个极限的解。解的性质取决于吸力参数。此外，利用四阶龙格-库塔格式结合打靶法，获得了数值解。
英文摘要：
This paper deals with the two-dimensional incompressible, laminar, steady-state boundary layer equations.First, we determine a family of velocity distributions outside the boundary layer such that these problems may have similarity solutions.Then, We examine in detail new exact solutions, called {\it Pseudo-similarity}, where the external velocity varies inversely-linear with the distance in the $x$-direction along the surface ($U_e(x) = U_\infty x^{-1}). $ The analysis shows that solutions exist only for a lateral suction. Here it is assumed that the flow is induced by a continuous permeable surface with the stretching velocity $ U_wx^{-1}.$ For specified conditions, we establish the existence of an infinite number of solutions, including monotonic solutions and solutions which oscillate an infinite number of times and tend to a certain limit. The properties of solutions depend on the suction parameter. Furthermore, making use of the fourth-order Runge-Kutta scheme together with the shooting method, numerical solutions are obtained.
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