Aerodynamic shape optimization using first and second Order adjoint and direct approaches

Papadimitriou, DI; Giannakoglou, KC

dc.contributor.author	Papadimitriou, DI	en
dc.contributor.author	Giannakoglou, KC	en
dc.date.accessioned	2014-03-01T01:27:50Z
dc.date.available	2014-03-01T01:27:50Z
dc.date.issued	2008	en
dc.identifier.issn	1134-3060	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18600
dc.subject	Adjoint Method	en
dc.subject	Entropy Generation	en
dc.subject	Objective Function	en
dc.subject	Performance Optimization	en
dc.subject	Point of View	en
dc.subject	Pressure Distribution	en
dc.subject	Shape Optimization	en
dc.subject	Direct Differentiation Method	en
dc.subject	Quasi Newton	en
dc.subject	Second Order	en
dc.subject.classification	Computer Science, Interdisciplinary Applications	en
dc.subject.classification	Engineering, Multidisciplinary	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.other	Adjoint	en
dc.subject.other	Adjoint approaches	en
dc.subject.other	Adjoint formulations	en
dc.subject.other	Adjoint methods	en
dc.subject.other	Aerodynamic shape optimizations	en
dc.subject.other	Cascade flows	en
dc.subject.other	Design variables	en
dc.subject.other	Direct approaches	en
dc.subject.other	Direct differentiation methods	en
dc.subject.other	Direct differentiations	en
dc.subject.other	Entropy generations	en
dc.subject.other	Field integrals	en
dc.subject.other	Hessian matrices	en
dc.subject.other	Inverse designs	en
dc.subject.other	Objective functions	en
dc.subject.other	Optimization schemes	en
dc.subject.other	Quasi newtons	en
dc.subject.other	Second orders	en
dc.subject.other	Second-order sensitivities	en
dc.subject.other	Sensitivity expressions	en
dc.subject.other	Solid walls	en
dc.subject.other	Total pressures	en
dc.subject.other	Viscous loss	en
dc.subject.other	Aerodynamics	en
dc.subject.other	Distribution functions	en
dc.subject.other	Functions	en
dc.subject.other	Inverse problems	en
dc.subject.other	Shape optimization	en
dc.title	Aerodynamic shape optimization using first and second Order adjoint and direct approaches	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s11831-008-9025-y	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s11831-008-9025-y	en
heal.language	English	en
heal.publicationDate	2008	en
heal.abstract	This paper focuses on discrete and continuous adjoint approaches and direct differentiation methods that can efficiently be used in aerodynamic shape optimization problems. The advantage of the adjoint approach is the computation of the gradient of the objective function at cost which does not depend upon the number of design variables. An extra advantage of the formulation presented below, for the computation of either first or second order sensitivities, is that the resulting sensitivity expressions are free of field integrals even if the objective function is a field integral. This is demonstrated using three possible objective functions for use in internal aerodynamic problems; the first objective is for inverse design problems where a target pressure distribution along the solid walls must be reproduced; the other two quantify viscous losses in duct or cascade flows, cast as either the reduction in total pressure between the inlet and outlet or the field integral of entropy generation. From the mathematical point of view, the three functions are defined over different parts of the domain or its boundaries, and this strongly affects the adjoint formulation. In the second part of this paper, the same discrete and continuous adjoint formulations are combined with direct differentiation methods to compute the Hessian matrix of the objective function. Although the direct differentiation for the computation of the gradient is time consuming, it may support the adjoint method to calculate the exact Hessian matrix components with the minimum CPU cost. Since, however, the CPU cost is proportional to the number of design variables, a well performing optimization scheme, based on the exactly computed Hessian during the starting cycle and a quasi Newton (BFGS) scheme during the next cycles, is proposed. © 2008 CIMNE, Barcelona, Spain.	en
heal.publisher	SPRINGER	en
heal.journalName	Archives of Computational Methods in Engineering	en
dc.identifier.doi	10.1007/s11831-008-9025-y	en
dc.identifier.isi	ISI:000260306400002	en
dc.identifier.volume	15	en
dc.identifier.issue	4	en
dc.identifier.spage	447	en
dc.identifier.epage	488	en