UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

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2022-07-01 16:58

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Conference: Bucharest University Faculty of Physics 2019 Meeting


Section: Theoretical Physics and Applied Mathematics


Title:
An efficient numerical scheme for two singular integral equations with Hilbert-type kernel


Authors:
Adrian STOICA


Affiliation:
University of Bucharest, Faculty of Physics


E-mail
adst21@yahoo.com


Keywords:
non-planar wing, singular integral, collocation-quadrature method


Abstract:
The study of an incompressible flow past a non-planar elliptic ring-shaped wing leads to solving a singular integral equation where the cross-sectional circulation is the unknown. The kernel of this equation can be decomposite into a regular part and a singular one. The singular part is either of Hilbert type, like in the case of the problem of the non-planar wing of minimum induced drag, or the derivative of a kernel of Hilbert type, like in the case of the lifting line equation for non-planar wings. In this paper we propose a collocation-quadrature method for solving this type of equations. The method is tested successfully for two analytically solvable cases.


References:

1) Belotserkovsky,S.M., Lifanov,I.K.: Method of discrete vortices, CRC Press (1993)

2) Demasi, L., Chiocchia,G., Carrera,E.: Aerodinamica dei sistemi portanti chiusi: ala anulare ellittica, Italian Conference AIDAA Roma, 15-19th Sept. (2003)

3) Demasi, L., Monegato, G., Dipace, A., Cavallaro, R.: Minimum induced drag theorems for joined wings, closed systems, and generic biwings: theory. J. Optim. Theory Appl. 169(1), 200–235 (2016)