Shape Optimization in Pipe

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Ghalavandi, Ebrahim | 2015

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 47532 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Fotouhi Firouzabad, Morteza
Abstract:
Shape optimization can be viewed as a part of the important branch of computational mechanics called structural optimization. In structural optimization problems one tries to set up some data of the mathematical model that describe the behavior of a structure in order to find a situation in which the structure exhibits a priori given properties. Nowadays shape optimization represents a vast scientific discipline involving all problems in which the geometry (in a broad sense) is subject to optimization. The problem has to be well posed from the mechanical point of view, requiring a good understanding of the physical background. Then one has to find an appropriate mathematical model that can be used for the numerical realization. We consider an incompressible fluid in a three-dimensional pipe, following the Navier–Stokes system with classical boundary conditions. We prove that there exists an optimal shape for the criterion energy dissipated by the fluid but the cylinder is not optimal.At last, we show some numerical simulations for that problem
Keywords:
Shape Optimization ; Navier-Stokes Equation ; PIPES ; Energy Dissipation ; Augmented-Lagrangian Method

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