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A contractive operator solution of an airfoil design inverse problem
Author(s) -
Šimák Jan,
Pelant Jaroslav
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700136
Subject(s) - mathematics , airfoil , mathematical analysis , jacobian matrix and determinant , newton's method , operator (biology) , euler equations , nonlinear system , physics , mechanics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene
This paper deals with a numerical method for an airfoil design which was presented in [3, 5]. This method is intended for design of an airfoil from a given velocity distribution along a mean camber line. The method is based on searching for a fixed point of a contractive operator. This operator combines an inexact inverse operator and equations describing the flow. A subsonic flow is assumed, the flow is described by a system of the Euler equations which is solved by an implicit finite volume method. The Newton method is applied to the solution of the nonlinear system. The resulting system of linear algebraic equations is solved by GMRES method, the Jacobian‐free version is described. The inexact inverse operator consists of a middle curve function and a thickness function, both depending on the given velocity distribution. In addition to the velocity distribution the velocity in infinity is given. The angle of attack is determined so that the stagnation point is in a specific position. Successful numerical results are presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)