Three Dimensional Large Scale Aerodynamic Shape Optimization based on Shape Calculus

Schmidt, Stephan; Gauger, Nicolas R.; Ilić, Časlav; Schulz, Volker

doi:10.2514/6.2011-3718

Cited by 39 publications

(44 citation statements)

References 20 publications

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“…Analytical approximate Hessians that do not require second-order flow sensitivities have been formulated for inverse design problems due to their quadratic nature [22,46]. The idea of gradient smoothing using Sobolev gradients [23] has extended to more complex approximate Hessians via shape calculus and Fourier analysis [2,48]. With the advent of automatic differentiation (AD), exact second-order sensitivities [51,38,14] have been employed in ASO problems.…”

Section: The Hessianmentioning

confidence: 99%

Approximate Hessian for accelerated convergence of aerodynamic shape optimization problems in an adjoint-based framework

Shi-Dong

Nadarajah

2018

Computers & Fluids

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Section: The Hessianmentioning

confidence: 99%

Approximate Hessian for accelerated convergence of aerodynamic shape optimization problems in an adjoint-based framework

Shi-Dong

Nadarajah

2018

Computers & Fluids

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“…This can be done on the one hand for the Navier-Stokes equations in pointwise form as stated in equation (9.14), see [14,15]. On the other hand the shape gradient can be computed for the Navier-Stokes equations in variational form…”

Section: Theorem 2 (Hadamard Theorem) For Every Domain ω ⊂ D Let J (mentioning

confidence: 99%

“…For the optimization the scalar distribution g(Γ ), which corresponds to the shape gradient, has to be found for the drag and lift coefficient. Proof A proof can be found in [14].…”

Section: Theorem 2 (Hadamard Theorem) For Every Domain ω ⊂ D Let J (mentioning

confidence: 99%

Adaptive Aerodynamic Design Optimization for Navier-Stokes Using Shape Derivatives with Discontinuous Galerkin Methods

Kaland

Sonntag

Gauger

2014

Computational Methods in Applied Sciences

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We state and analyze one-shot optimization methods in a function space setting for optimal control problems, for which the state equation is given in terms of a fixed-point equation. Further, we concentrate on the application of a design optimization problem incorporating the solution of the compressible Navier-Stokes equations using a discontinuous Galerkin method. For the given primal fixed-point solver an appropriate adjoint solver is constructed. For the following design update we compute the shape derivative analytically based on the weak formulation of the governing equations. The primal, adjoint and design updates are performed in a oneshot manner, i.e., the corresponding equations are not fully solved, instead only a few iteration steps are performed. Finally, we add an additional adaptive step. During the optimization routine we refine or coarsen the grid to obtain a better accuracy.

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“…3 for an illustration). This enables the definition of the shape derivative of the shape functional J at Ω in direction of a vector field V by [6,26,27], it is known that the shape gradient g can be expressed as a boundary integral of the form…”

Section: Shape Optimizationmentioning

confidence: 99%

Optimization of current carrying multicables

Harbrecht

Loos

2015

Comput Optim Appl

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Intense electric currents in cable bundles contribute to hotspot generation and overheating of essential car elements, especially in connecting structures. An important aspect in this context is the influence of the positioning of wires in cable harnesses. In order to find an appropriate multicable layout with minimized maximum temperatures, we formulate an optimization problem. Depending on the packing density of the cable bundle, it is solved via different optimization strategies: in case of loosely packed cable bundles solely by a gradient based strategy (shape optimization), densely packed ones by arrangement heuristics combined with a standard genetic algorithm, others by mixed strategies.In the simulation model, the temperature dependence of electric resistances and different parameter values for the multitude of subdomains are respected. Convective and radiative effects are summarized by a heat transfer coefficient in a nonlinear boundary condition. Finite elements in combination with an interior-point method and a genetic algorithm allow the solution of the optimization problem for a large number of cable bundle types. Furthermore, we present an adjoint method for the solution of the shape optimization problem. The jumps at the interfaces of different materials are essential for the Hadamard representation of the shape gradient. Numerical experiments are carried out to demonstrate the feasibility and scope of the present approach.

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Three Dimensional Large Scale Aerodynamic Shape Optimization based on Shape Calculus

Cited by 39 publications

References 20 publications

Approximate Hessian for accelerated convergence of aerodynamic shape optimization problems in an adjoint-based framework

Approximate Hessian for accelerated convergence of aerodynamic shape optimization problems in an adjoint-based framework

Adaptive Aerodynamic Design Optimization for Navier-Stokes Using Shape Derivatives with Discontinuous Galerkin Methods

Optimization of current carrying multicables

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