Shape Optimization of a Coupled Thermal Fluid-Structure Problem in a Level Set Mesh Evolution Framework
| Autor: | Felipe Bordeu, Florian Feppon, Grégoire Allaire, Charles Dapogny, Julien Cortial |
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| Přispěvatelé: | Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Safran Tech, Calcul des Variations, Géométrie, Image (CVGI ), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
fluid structure interaction
Control and Optimization adjoint methods 010103 numerical & computational mathematics 01 natural sciences Domain (mathematical analysis) Level set Hadamard transform Fluid–structure interaction Applied mathematics Topology and shape optimization [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Shape optimization 0101 mathematics Mathematics Numerical Analysis AMS: 74P10 76B75 74F10 35Q79 65N50 Steady state Applied Mathematics Topology optimization 010101 applied mathematics convective heat transfer Modeling and Simulation [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Convection–diffusion equation adaptive remeshing [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] |
| Zdroj: | SeMA Journal: Boletin de la Sociedad Española de Matemática Aplicada SeMA Journal: Boletin de la Sociedad Española de Matemática Aplicada, Springer, 2019, 76 (3), pp.413-458. ⟨10.1007/s40324-018-00185-4⟩ SeMA Journal: Boletin de la Sociedad Española de Matemática Aplicada, 2019, 76 (3), pp.413-458. ⟨10.1007/s40324-018-00185-4⟩ |
| ISSN: | 2254-3902 2281-7875 |
| DOI: | 10.1007/s40324-018-00185-4⟩ |
| Popis: | International audience; Hadamard's method of shape differentiation is applied to topology optimization of a weakly coupled three physics problem. The coupling is weak because the equations involved are solved consecutively, namely the steady state Navier-Stokes equations for the fluid domain, first, the convection diffusion equation for the whole domain, second, and the linear thermo-elasticity system in the solid domain, third. Shape sensitivities are derived in a fully Lagrangian setting which allows us to obtain shape derivatives of general objective functions. An emphasis is given on the derivation of the adjoint interface condition dual to the one of equality of the normal stresses at the fluid solid interface. The arguments allowing to obtain this surprising condition are specifically detailed on a simplified scalar problem. Numerical test cases are presented using the level set mesh evolution framework of [4]. It is demonstrated how the implementation enables to treat a variety of shape optimization problems. keywords. Topology and shape optimization, adjoint methods, fluid structure interaction, convective heat transfer, adaptive remeshing. |
| Databáze: | OpenAIRE |
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