Shape Optimal Design Problem with Convective and Radiative Heat Transfer: Analysis and Implementation

Chenais, Denise; Monnier, Jérôme; Vila, Jean‐Paul

doi:10.1023/a:1017543529204

Cited by 11 publications

(14 citation statements)

References 3 publications

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“…Also, we define the derivative with respect to the domain in a classical manner as the derivative of the transported function with respect to the transformation, see (29). We refer to References [2,5,11,17,[19][20][21][22][23].…”

Section: Domain Variations and Shape Derivativesmentioning

confidence: 99%

“…In the present configuration, the boundary part # G G 0 is fixed and we seek to optimize the shape of # G G: A such situation arises in many problems like for example in the cooling problem studied in Reference [2] or in the minimization drag problem studied in Reference [5]. that an open set with a Lipschitz boundary has an external normal n almost everywhere, and boundary integrals can be defined.…”

Section: Domain Variations and Shape Derivativesmentioning

confidence: 99%

“…As an industrial application, one can cite the cooling problem under a car bonnet studied in References [1,2], or other shape optimal design problems in a forced convection flow based on the present radiative model. Many authors studied shape optimal design problems in a Navier-Stokes flow without heat transfer, steady state or not, and using gradient-type algorithm, see e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Shape optimal design problems in a Navier-Stokes flow with convective and diffusive heat transfer have been studied for example in References [8,9]. In Reference [2], the authors study a shape optimal design problem in a potential flow coupled with the present thermal model.…”

Section: Introductionmentioning

confidence: 99%

“…We present the optimization process required to solve numerically the shape inverse problem. We refer to Reference [10] for a detailed finite-element discretization of the present thermal model and to References [2,11] for the details of implementation of the shape problem.…”

Section: Introductionmentioning

confidence: 99%

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Shape sensitivities in a Navier‐Stokes flow with convective and grey bodies radiative thermal transfer

Monnier¹

2003

Optim Control Appl Methods

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SUMMARYWe study a shape optimal design problem for a forced convection flow: the steady-state Navier-Stokes equations coupled with an integro-differential thermal model. The thermal transfers are convective, diffusive and radiative with multiple reflections (model of grey bodies, radiosity equation). The inverse problem consists in minimizing a smooth cost function which depends on the solution, with respect to the domain of the equations. We prove the differentiability of the solution with respect to the domain. It follows the cost function differentiability. We introduce the adjoint state equation and obtain the exact differential of the cost function. The computational method of shape sensitivities and the optimization process are presented too.

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Section: Domain Variations and Shape Derivativesmentioning

confidence: 99%

Section: Domain Variations and Shape Derivativesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Shape sensitivities in a Navier‐Stokes flow with convective and grey bodies radiative thermal transfer

Monnier¹

2003

Optim Control Appl Methods

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The application of adjoint method for shape optimization in Stokes–Oseen flow

Yan

Gao

2016

Math Methods in App Sciences

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This paper presents a numerical method for shape optimization of a body immersed in an incompressible viscous flow governed by Stokes–Oseen equations. The purpose of this work is to optimize the shape that minimizes a given cost functional. Based on the continuous adjoint method, the shape gradient of the cost functional is derived by involving a Lagrangian functional with the function space parametrization technique. Then, a gradient‐type algorithm is applied to the shape optimization problem. The numerical examples indicate the proposed algorithm is feasible and effective in low Reynolds number flow. Copyright © 2016 John Wiley & Sons, Ltd.

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Shape optimization in the Navier‐Stokes flow with thermal effects

Yan

Gao

2013

Numerical Methods Partial

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In this article, we consider the shape optimization problem of a body immersed in the incompressible fluid governed by Navier-Stokes equations coupling with a thermal model. Based on the continuous adjoint method, we formulate and analyze the shape optimization problem. Then we derive the structure of shape gradient for the cost functional by using the differentiability of a minimax formulation involving a Lagrange functional with the function space parametrization technique. Moreover, we present a gradient-type algorithm to the shape optimization problem. Finally, numerical examples demonstrate the feasibility and effectiveness of the proposed algorithm.

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Shape Optimal Design Problem with Convective and Radiative Heat Transfer: Analysis and Implementation

Cited by 11 publications

References 3 publications

Shape sensitivities in a Navier‐Stokes flow with convective and grey bodies radiative thermal transfer

Shape sensitivities in a Navier‐Stokes flow with convective and grey bodies radiative thermal transfer

The application of adjoint method for shape optimization in Stokes–Oseen flow

Shape optimization in the Navier‐Stokes flow with thermal effects

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