Solving inverse problems involving the Navier–Stokes equations discretized by a Lagrange–Galerkin method |
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Affiliation: | 1. Department of Mathematics, Nazarbayev University, Astana, Kazakhstan;2. Department of Economics, Management, and Quantitative Methods, University of Milan, Milan, Italy;3. School of Accounting, Economics and Finance, University of Wollongong, Wollongong, Australia;4. Department of Mathematics and Statistics, Acadia University, Wolfville, Canada;5. Department of Economics and Statistics “Cognetti de Martiis”, University of Turin, Torino, Italy |
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Abstract: | In this article, we are investigating the numerical approximation of an inverse problem involving the evolution of a Newtonian viscous incompressible fluid described by the Navier–Stokes equations in 2D. This system is discretized using a low order finite element in space coupled with a Lagrange–Galerkin scheme for the nonlinear advection operator. We introduce a full discrete linearized scheme that is used to compute the gradient of a given cost function by ensuring its consistency. Using gradient based optimization algorithms, we are able to deal with two fluid flow inverse problems, the drag reduction around a moving cylinder and the identification of a far-field velocity using the knowledge of the fluid load on a rectangular bluff body, for both fixed and prescribed moving configurations. |
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