CONTINUOUS ADJOINT METHODS IN SHAPE , TOPOLOGY , FLOW-CONTROL AND ROBUST OPTIMIZATION Open Source CFD International Conference , London 2012

Recent progress in the development of continuous adjoint methods for the computation of the firstand higher-order sensitivity derivatives of various objective functions in aero/hydrodynamics is presented. Regarding development of methods, this paper includes: (a) The continuous adjoint to low-Reynolds turbulence models by laying emphasis on the need to include the adjoint turbulence model equations into the optimization loop. (b) The continuous adjoint to turbulent flow solvers which use the wall function technique. (c) The truncated Newton method which relies on the computation of Hessian-vector products, as a more efficient alternative to the exact Newton method, in problems with many design variables. (d) The adjoint method for the solution of robust design problems, based on the second-order second-moment (SOSM) approach and a gradient-based algorithm, requiring the computation of up to third-order mixed derivatives w.r.t. the environmental and design variables. Regarding applications, the adjoint method is demonstrated in aero/hydrodynamic shape optimization problems, the optimization of steady/unsteady jetbased flow control systems and topology optimization problems in fluid mechanics. Steady and unsteady continuous adjoint methods are employed. Most of the methods presented in this paper have been implemented in OpenFOAM c ©, adding state of the art optimization capabilities to a widely used open source software. K. C. Giannakoglou, D. I. Papadimitriou, E. M. Papoutsis, I. S. Kavvadias, C. Othmer 1 AERODYNAMIC OPTIMIZATION IN TURBULENT FLOWS 1.1 Flow Equations and Objective Functions The system of state equations are presented in a way which covers shape, topology and flow control optimization problems. To do so, some extra terms depending on the porosity field α are appended to the Navier-Stokes equations. The new terms are useful only in topology optimization; otherwise, α ≡ 0. The flow is incompressible and, without loss in generality, the Spalart-Allmaras turbulence model, [1], is used to effect closure in turbulent flows. Based on the above, the state equations are written as R = 0, Ri = 0, R = 0, R = 0 (1)

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