Solving inverse problems involving the Navier–Stokes equations discretized by a Lagrange–Galerkin method. (English) Zbl 1112.74443
Summary: 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.
MSC:
| 74M10 | Friction in solid mechanics |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
Keywords:
Navier-Stokes equations; ALE formulation; Lagrange-Galerkin; characteristics; inverse problem; quasi-Newton methods; optimal boundary control of the tracking type.References:
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