论文标题
周期域中流量的演算
A calculus for flows in periodic domains
论文作者
论文摘要
我们提出了一个建设性的程序，用于计算每个周期窗口有多个边界的周期域中的2-D电势流。该解决方案需要两个步骤：（i）从规范圆形域到物理目标结构域的保形映射，以及（ii）圆形域内的复杂电势的构造。所有单一周期域都可以分为三种不同的类型：在两个方向上无限制，在一个方向上无限制，并且有限。在每种情况下，我们将目标周期域通过共形映射与规范的圆形域相关联，并为每种类型的目标域提供了典型的共形图的功能形式。然后，我们提出了一系列潜在流动现象的解决方案，包括流动奇点，移动边界，均匀的流动，紧张的流量和循环流。通过根据超验Schottky（Klein Prime函数）来逐渐衡量解决方案，随后的解决方案对于每个时期窗口的任意障碍物有效。此外，我们的解决方案是精确的，不需要任何渐近近似。
We present a constructive procedure for the calculation of 2-D potential flows in periodic domains with multiple boundaries per period window. The solution requires two steps: (i) a conformal mapping from a canonical circular domain to the physical target domain, and (ii) the construction of the complex potential inside the circular domain. All singly periodic domains may be classified into three distinct types: unbounded in two directions, unbounded in one direction, and bounded. In each case, we relate the target periodic domain to a canonical circular domain via conformal mapping and present the functional form of prototypical conformal maps for each type of target domain. We then present solutions for a range of potential flow phenomena including flow singularities, moving boundaries, uniform flows, straining flows and circulatory flows. By phrasing the solutions in terms of the transcendental Schottky--Klein prime function, the ensuing solutions are valid for an arbitrary number of obstacles per period window. Moreover, our solutions are exact and do not require any asymptotic approximations.
