An adjoint method for shape optimization in unsteady viscous flows

Srinath, D.N.; Mittal, Sanjay

doi:10.1016/j.jcp.2009.11.019

Cited by 50 publications

(21 citation statements)

References 46 publications

(51 reference statements)

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“…Recently, there have been several successful attempts using the adjoint equations in shape optimization (Kuruvila et al, 1994;Anderson and Venkatakrishnan, 1999;Giles and Pierce, 2000;Jameson, 2001;Brezillon and Gauger, 2004;Giering et al, 2005;Carpentieri et al, 2007;Zymaris et al, 2009;Peter and Dwight, 2010;Srinath and Mittal, 2010;Zymaris et al, 2010;Jameson and Ou, 2011), optimal boundary control (Bewley et al, 2001;Collis et al, 2000;Collis et al, 2004) and optimal noise control (Cerviño and Bewley, 2002;Joslin et al, 2005;Wei and Freund, 2006;Spagnoli and Airiau, 2008;Babucke et al, 2009;Kim et al, 2010;Rumpfkeil and Zingg, 2010;Schulze et al, 2011). However, because of the expensive iterative optimization procedure, which involves solving the adjoint equations backward in time and which necessitates the storage of the flow fields obtained during the solution of the Navier-Stokes equations, calculations for the purpose of noise reduction have been carried out almost exclusively for 2D-DNS only and recently for 3D-LES in Kim et al (2010).…”

Section: Introductionmentioning

confidence: 99%

Investigation of a continuous adjoint-based optimization procedure for aeroacoustic control of plane jets

Marinc

Foysi

2012

International Journal of Heat and Fluid Flow

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Section: Introductionmentioning

confidence: 99%

Investigation of a continuous adjoint-based optimization procedure for aeroacoustic control of plane jets

Marinc

Foysi

2012

International Journal of Heat and Fluid Flow

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“…A close up view of a typical finite element mesh used for computations is shown in Figure . The mesh is similar to that used in our earlier studies .…”

Section: Resultsmentioning

confidence: 99%

“…Table shows that the airfoils with high values of lift coefficient are associated with seemingly unconventional shapes. Srinath and Mittal carried out an optimization study at Re = 1000 and α = 4° to obtain an airfoil with a desired time‐averaged lift coefficient. The objective function for this inverse problem is

I_{normalc} MathClass-rel= (1 MathClass-bin∕ 2) {(\overset{C_{normall}}{falsemml-overline} MathClass-bin- C_{normall 0})}^{2}

, where C l0 is the desired value of the time‐averaged lift coefficient.…”

Section: Resultsmentioning

confidence: 99%

A method to carry out shape optimization with a large number of design variables

Kumar

Diwakar

Attree

et al. 2012

Numerical Methods in Fluids

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SUMMARYA new method for shape optimization with relatively large number of design variables is proposed. It is well known that gradient‐based methods converge to a local optimum. As a result, utilization of a richer design space does not necessarily lead to a better design. This is demonstrated via the design of an airfoil for maximum lift for Re = 1000 and α = 4° flow. The airfoil is represented by fourth‐order non‐uniform rational B‐splines, and the control points are used as design variables. Starting with a NACA0012 airfoil, it is found that the optimal airfoil obtained with 13 control points has far superior aerodynamic performance than the ones obtained with 39 and 61 control points. For effective utilization of a richer design space, it is proposed that the number of design variables be increased gradually. The method is demonstrated by designing high lift airfoils for Re = 1000 and 1 × 104. The objective function is the maximization of the time‐averaged lift coefficient for α = 4°. The optimization cycle with 27 control points is initiated with the optimal airfoil obtained with 13 control points. The process is continued with gradual increase in the number of design variables. Beyond a certain number of control points, the optimization leads to a spontaneous appearance of corrugations on the upper surface of the airfoil. The corrugations are responsible for the generation of small vortices that add to the suction on the upper surface of the airfoil and lead to enhanced lift. A stabilized finite element method is used to solve the unsteady flow and adjoint equations. Copyright © 2012 John Wiley & Sons, Ltd.

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“…A similar approach of an adjoint variable has been used in many applications [19][20][21][22][23][24]. We choose this method because of its computational cost reduction in comparison with the conventional method of perturbations or with the method of sensitivity equation.…”

Section: Inverse Problemmentioning

confidence: 99%