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Shape optimization for the generalized Graetz problem

Abstract : We apply shape optimization tools to the generalized Graetz problem which is a convection-diffusion equation. The problem boils down to the optimization of generalized eigen values on a two phases domain. Shape sensitivity analysis is performed with respect to the evolution of the interface between the fluid and solid phase. In particular physical settings, counterexamples where there is no optimal domains are exhibited. Numerical examples of optimal domains with different physical parameters and constraints are presented. Two different numerical methods (level-set and mesh-morphing) are show-cased and compared.
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Submitted on : Monday, February 17, 2014 - 2:43:34 PM
Last modification on : Friday, December 24, 2021 - 3:18:04 PM
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Frédéric de Gournay, Jérôme Fehrenbach, Franck Plouraboué. Shape optimization for the generalized Graetz problem. Structural and Multidisciplinary Optimization, Springer Verlag (Germany), 2014, ⟨10.1007/s00158-013-1032-4⟩. ⟨hal-00947878⟩

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