Abstract
An algorithm is presented for the computation of a conformal mapping discretized on a non-uniformly spaced point set, useful for the numerical solution of many problems of fluid dynamics. Most existing iterative techniques, both those having a linear and those having a quadratic type of convergence, rely on the fast Fourier transform ( FFT) algorithm for calculating a convolution integral which represents the most time-consuming phase of the computation. The FFT, however, definitely cannot be applied to a non-uniform spacing. The algorithm presented in this paper has been made possible by the construction of a calculation method for convolution integrals which, despite not using an FFT, maintains a computation time of the same order as that of the FFT. The new technique is successfully applied to the problem of conformally mapping a closely spaced cascade of airfoils onto a circle, which requires an exceedingly large number of points if it is solved with uniform spacing.
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