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Variational Methods in Design Optimization and Sensitivity Analysis for Two-Dimensional Euler EquationsVariational methods (VM) sensitivity analysis employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.
Document ID
19970017777
Acquisition Source
Langley Research Center
Document Type
Contractor Report (CR)
Authors
Ibrahim, A. H. (Old Dominion Univ. Norfolk, VA United States)
Tiwari, S. N. (Old Dominion Univ. Norfolk, VA United States)
Smith, R. E. (NASA Langley Research Center Hampton, VA United States)
Date Acquired
September 6, 2013
Publication Date
April 1, 1997
Subject Category
Aircraft Design, Testing And Performance
Report/Patent Number
NAS 1.26:204431
ODU/ICAM-97-102
NASA-CR-204431
Accession Number
97N19897
Funding Number(s)
CONTRACT_GRANT: NCC1-232
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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