Computation of plane potential flow in multiple connected domains using series methods and conformal mapping

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Mears, Justin Laurence
DeLillo, Thomas K.

This paper presents a method for calculating potential flow in the exterior of multiplyconnected circle domains in the complex plane. The method employs a Laurent series expansion of the potential function on the circular boundaries, which can be easily written into a linear system for finding the Laurent coefficients. This system exhibits the form of “identity plus a low-rank matrix”, enabling efficient utilization of conjugate-gradient-like methods.

Through the use of conformal mapping, the method is extended to calculate the potential flow in multiply-connected domains exterior to any closed curves. This is achieved by computing the potential flow over an appropriate circle domain and mapping this result to the desired physical domain using an approximation of the Laurent series for the conformal map. Circulations around each boundary can be specified or calculated, with a specific focus on multi-element airfoils where the circulations are determined to satisfy the Kutta condition at trailing edges.

Comparisons with alternatives methods for computing flow in circle domains, namely reflection and least-squares methods, are included to demonstrate the accuracy and efficiency of the new method. Finally, there are many examples of flow calculations over multiplyconnected regions with smooth boundaries and multi-element airfoils.

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Thesis (Ph.D.)-- Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics, and Physics