This article is cited in 1 paper

Application in aerohydrodynamics of the solution of an inverse boundary value problem for analytic functions

R. B. Salimov

Kazan State University of Architecture and Engineering, 1 Zelenaya str., 420043 Kazan

Abstract: We consider a modified inverse boundary value problem of aerohydrodynamics in which it is required to find the shape of an airfoil streamlined by a potential flow of an incompressible nonviscous fluid, when the distribution of the velocity potential on one section of the airfoil is given as a function of the abscissa, while, on other sections of the airfoil, as a function of the ordinate of the point. The velocity of the undisturbed flow streamlining the sought-for airfoil is determined in the process of solving the problem. It is shown that, under rather general conditions on the initially set functions, the sought-for contour is closed unlike the inverse problem in the case when, on the unknown contour, the velocity distribution is given as a function of the arc abscissa of the contour point. We also consider the case when, on the entire desired contour, the distribution of the velocity potential is given as a function of one and the same Cartesian coordinate of the contour point.

Keywords: inverse boundary value problems of aerodynamics, analytic function, conformal mapping, airfoil.

UDC: 517.54

Received: 08.08.2016

DOI: 10.17377/sibjim.2018.21.108

 English version: Journal of Applied and Industrial Mathematics, 2018, 12:1, 136–144

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