Shape optimisation for the wave-making resistance of a submerged body

Abstract : In this thesis, we compute the shape of a fully immersed object with a given area which minimises the wave resistance. The smooth body moves at a constant speed under the free surface of a fluid which is assumed to be inviscid and incompressible. The wave resistance is the drag, i.e. the horizontal component of the force exerted by the fluid on the obstacle. We work with the 2D Neumann-Kelvin equations, which are obtained by linearising the irrotational Euler equations with a free surface. The Neumann-Kelvin problem is formulated as a boundary integral equation based on a fundamental solution which handles the linearised free surface condition. We use a gradient descent method to find a local minimiser of the wave resistance problem. A gradient with respect to the shape is calculated by a boundary variation method. We use a level-set approach to calculate the wave-making resistance and to deal with the displacements of the boundary of the obstacle. We obtain a great variety of optimal shapes depending on the depth of the object and its velocity.
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Evi Noviani. Shape optimisation for the wave-making resistance of a submerged body. Mathematical Physics [math-ph]. Université de Poitiers, 2018. English. ⟨NNT : 2018POIT2298⟩. ⟨tel-02139092⟩

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