The continuous direct-adjoint approach for second order sensitivities in viscous aerodynamic inverse design problems

Papadimitriou, DI; Giannakoglou, KC

dc.contributor.author	Papadimitriou, DI	en
dc.contributor.author	Giannakoglou, KC	en
dc.date.accessioned	2014-03-01T01:32:03Z
dc.date.available	2014-03-01T01:32:03Z
dc.date.issued	2009	en
dc.identifier.issn	0045-7930	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20040
dc.subject	Newton Method	en
dc.subject	Objective Function	en
dc.subject	Pressure Distribution	en
dc.subject	Viscous Flow	en
dc.subject	Direct Differentiation Method	en
dc.subject	First Order	en
dc.subject	Second Order	en
dc.subject.classification	Computer Science, Interdisciplinary Applications	en
dc.subject.classification	Mechanics	en
dc.subject.other	DATA ASSIMILATION	en
dc.subject.other	OPTIMIZATION	en
dc.subject.other	DERIVATIVES	en
dc.title	The continuous direct-adjoint approach for second order sensitivities in viscous aerodynamic inverse design problems	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.compfluid.2008.12.007	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.compfluid.2008.12.007	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	A novel continuous adjoint approach for the computation of the second order sensitivities of the objective function used in inverse design problems is proposed. In the framework of the Newton method, the proposed approach can be used to efficiently cope with inverse design problems in Viscous flows, where the target is a given pressure distribution along the solid walls. It consists of two steps and will, thus, be referred to as the direct-adjoint approach. At the first step, the direct differentiation method is used to compute the first order sensitivities of the flow variables with respect to the design variables and build the gradient of the objective function. At the second step, the adjoint approach is used to compute the second order sensitivities. The final Hessian expression is free of field integrals and its computation requires the solution of N + 1 equivalent flow (system) Solutions for N design variables. Since the CPU cost of using the Newton method, with exact gradient and Hessian data at each cycle, becomes prohibitively high, an approach that computes the exact Hessian only once and then updates it in an approximated manner through the BFGS formula, is used instead. The accuracy of the Hessian matrix components, computed using the direct-adjoint approach is demonstrated on the inverse design of a diffuser and a cascade airfoil. (C) 2008 Elsevier Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	COMPUTERS & FLUIDS	en
dc.identifier.doi	10.1016/j.compfluid.2008.12.007	en
dc.identifier.isi	ISI:000267201100005	en
dc.identifier.volume	38	en
dc.identifier.issue	8	en
dc.identifier.spage	1539	en
dc.identifier.epage	1548	en