Accession Number : ADA309055

Title :   Analysis of the Hessian for Aerodynamic Optimization: Inviscid Flow.

Descriptive Note : Contract rept.,

Corporate Author : INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

Personal Author(s) : Arian, Eyal ; Ta'asan, Shlomo

PDF Url : ADA309055

Report Date : APR 1996

Pagination or Media Count : 24

Abstract : In this paper we analyze inviscid aerodynamic shape optimization problems governed by the full potential and the Euler equations in two and three dimensions. The analysis indicates that minimization of pressure dependent cost functions results in Hessians whose eigenvalue distributions are identical for the full potential and the Euler equations. However the optimization problems in two and three dimensions are inherently different. While the two dimensional optimization problems are well-posed the three dimensional ones are ill-posed. Oscillations in the shape up to the smallest scale allowed by the design space can develop in the direction perpendicular to the flow, implying that a regularization is required. A natural choice of such a regularization is derived. The analysis also gives an estimate of the Hessian's condition number which implies that the problems at hand are ill-conditioned. Infinite dimensional approximations for the Hessians are constructed and preconditioners for gradient based methods are derived from these approximate Hessians.

Descriptors :   *OPTIMIZATION, *INVISCID FLOW, SIZES(DIMENSIONS), DISTRIBUTION, TWO DIMENSIONAL, SHAPE, EIGENVALUES, THREE DIMENSIONAL, APPROXIMATION(MATHEMATICS), AERODYNAMIC CHARACTERISTICS, EULER EQUATIONS, WINGS, OSCILLATION, AERODYNAMICS, GRADIENTS.

Subject Categories : Aerodynamics
      Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE