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Geometry optimization applied to incompressible fluid mechanics

Abstract : This applied mathematics thesis is dedicated to the modelling and exploration of numerical geometry optimization techniques. The first chapter is dedicated to a geometry optimization algorithm implemented in optiflow, in the case where the boundary to optimize is associated to no-slip conditions. The implementation is online and comes with a manual. It is therefore possible to use it for real-life applications such as pipeline or air conditioning, etc. In the second chapter, I describe a way to model fluid flow through an aquaporine. After making the fluid model precise, the existence of an optimal shape for the dissipated energy criterion is proven. Partial boundary conditions make appear difficulties in the sensitivity analysis of the optimization problem. A specific numerical treatment is presented to overcome this difficulty. Finally, several numerical examples are presented and commented.
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Submitted on : Tuesday, March 10, 2020 - 3:33:11 PM
Last modification on : Tuesday, January 19, 2021 - 3:18:43 AM
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  • HAL Id : tel-01918608, version 2


Florian Omnès. Geometry optimization applied to incompressible fluid mechanics. Analysis of PDEs [math.AP]. Sorbonne Université, 2018. English. ⟨NNT : 2018SORUS278⟩. ⟨tel-01918608v2⟩



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