Mathematics of Computation

Author(s): H. Berger; G. Warnecke; W. L. Wendland.
Journal: Math. Comp. 66 (1997), 1407-1440.
MSC (1991): Primary 65N30, 68N38, 76H05, 49M10, 35L67
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Abstract: A sensitive issue in numerical calculations for exterior flow problems, e.g.around airfoils, is the treatment of the far field boundary conditions on a computational domain which is bounded. In this paper we investigate this problem for two-dimensional transonic potential flows with subsonic far field flow around airfoil profiles. We take the artificial far field boundary in the subsonic flow region. In the far field we approximate the subsonic potential flow by the Prandtl-Glauert linearization. The latter leads via the Green representation theorem to a boundary integral equation on the far field boundary. This defines a nonlocal boundary condition for the interior ring domain. Our approach leads naturally to a coupled finite element/boundary element method for numerical calculations. It is compared with local boundary conditions. The error analysis for the method is given and we prove convergence provided the solution to the analytic transonic flow problem around the profile exists.

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H. Berger
Affiliation: Braunag F-1 TW4, Frankfurter Str 145, D-61476 Kronberg, Germany

G. Warnecke
Affiliation: Fakultät für Mathematik, Otto--von--Guericke--Universität Magdeburg, PF 4120, D--39016 Magdeburg, Germany
Email: gerald.warnecke@mathematik.uni-magdeburg.de

W. L. Wendland
Affiliation: Mathematisches Institut A, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
Email: wendland@mathematik.uni-stuttgart.de

DOI: 10.1090/S0025-5718-97-00878-8
PII: S 0025-5718(97)00878-8
Keywords: Transonic full potential equation, artificial boundary conditions, finite elements, boundary elements, asymptotic error analysis
Received by editor(s): August 13, 1993
Received by editor(s) in revised form: September 18, 1995
Additional Notes: The research reported in this paper was supported by the ``Stiftung Volkswagenwerk''.
Dedicated: This work is dedicated to Professor Dr. Klaus Kirchgässner on the occasion of his 60th birthday
Copyright of article: Copyright 1997, American Mathematical Society

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