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The aim of this work is to use isogeometric analysis, a unification of finite element methods (FEM) and computer aided design (CAD), to solve shape optimization problems within fluid mechanics. The flow problems considered are governed by the 2-dimensional steady-state, incompressible Navier-Stokes equations. The crux of isogeometric analysis is to approximate the fluid velocity and pressure fields by B-splines. The accurate geometry representation and high degree of continuity of the flow fields are some of the method's advantages. In shape optimization for fluids we search for an optimal design of the flow domain that minimizes a prescribed objective, while satisfying suitable constraints. The design variables in the isogeometric pproach are the coordinates of control points that define the boundary of the domain. With the ability to represent complex shapes in few design variables, and the unification of the analysis and geometry models, isogeometric analysis is highly suited for shape optimization purposes. The methodology is firstly presented through a simple example in which a pipe bend is designed to minimize the drag with a constraint on the area of the pipe. The basics of how to apply isogeometric analysis to the Navier-Stokes equations are briefly covered, some regularization methods to ensure good boundary parametrizations during optimization are discussed, and different design results for a range of Reynolds numbers are presented. Lastly, we present results for a simple airfoil optimization, in which an airfoil is designed to minimize the drag with a constraint on the lift and the size of the wing.
Place: Hurdalsjoen, Norway
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ID: 2374872