Solving inverse problems involving the Navier脙脙脙脙脙脙Stokes equations discretized by a Lagrange脙脙脙脙脙脙Galerkin method
- 作者：Fourestey ; Gilles ; Moubachir ; Marwan
- 关键词：28 ; 29 ; 41 ; 59 ; Navier脙脙脙脙脙脙Stokes equations ; ALE formulation ; Lagrange脙脙脙脙脙脙Galerkin ; Characteristics ; Inverse problem ; Quasi-Newton methods ; Optimal boundary control of the tracking type
- 刊名：Computer Methods in Applied Mechanics and Engineering
- 出版年：2005
- 期刊代码：27_00457825
- 类别：cp
- 出版时间：February 25, 2005
- 卷：194
- 期：6-8
- 页码：877-906
- 文件大小：727 K
摘要
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芒芒芒Stokes equations in 2D. This system is discretized using a low order finite element in space coupled with a Lagrange芒芒芒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.