Properties and Numerical Solution of an Integral Equation to Minimize Airplane Drag

Peter Junghanns (), Giovanni Monegato () and Luciano Demasi ()
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Peter Junghanns: Technische Universität Chemnitz, Fakultät für Mathematik
Giovanni Monegato: Politecnico di Torino, Dipartimento di Scienze Mathematiche
Luciano Demasi: San Diego State University, Department of Aerospace Engineering

A chapter in Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, 2018, pp 675-701 from Springer

Abstract: Abstract In this paper, we consider an (open) airplane wing, not necessarily symmetric, for which the optimal circulation distribution has to be determined. This latter is the solution of a constraint minimization problem, whose (Cauchy singular integral) Euler-Lagrange equation is known. By following an approach different from a more classical one applied in previous papers, we obtain existence and uniqueness results for the solution of this equation in suitable weighted Sobolev type spaces. Then, for the collocation-quadrature method we propose to solve the equation, we prove stability and convergence and derive error estimates. Some numerical examples, which confirm the previous error estimates, are also presented. These results apply, in particular, to the Euler-Lagrange equation and the numerical method used to solve it in the case of a symmetric wing, which were considered in the above mentioned previous papers.

Date: 2018
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DOI: 10.1007/978-3-319-72456-0_30

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