Conformal maps boundary conditions

The second boundary condition will change appropriately if another experiment than the potential jump is simulated. Here, rmax and 0max depend on the conformal map used, and on how / nax is chosen (see below). For MWA and VB, 0max = 7t/2, while for AF, it is unity. 

This is Laplace s equation in rectangular coordinates. If suitable boundary conditions exist or are known, Eq. (3.9-9) can be solved to give (x, y). Then the velocity at any point can be obtained using Eq. (3.9-5). Techniques for solving this equation include using numerical analysis, conformal mapping, and functions of a complex variable and are given elsewhere (B2, S3). Euler s equations can then be used to find the pressure distribution. 

There are both Irregular (I) and Regular (R) points at the intersections between the Smooth (S) and Critical (C) boundaries Bi and B2 in the WMBVP as illustrated in Fig. 2.6 where these two boundary intersection points are identified as Pi and P2. The classification of the boundary points Pi and P2 in Fig. 2.6 depends on (1) the boundary conditions Pi Pj) and (2) the continuity of the boundaries B and their derivatives where i, j, and m = 1 or 2. A conformal mapping of the semi-infinite wave channel strip in the physical plane will yield a Fredholm integral equation, where these critical points may be transformed to singular points that are integrable over a smooth continuous mapped boundary. 

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