We present a penalization parameter method for obstacle identification in an incompressible fluid flow for a modified version of the Oseen equations. The proposed method consist in adding a high resistance potential to the system such that some subset of its boundary support represents the obstacle. This allows to work in a fixed domain and highly simplify the solution of the inverse problem via some suitable cost functional. Existence of minimizers and first and second order optimality conditions are derived through the differentiability of the solutions of the Oseen equation with respect to the potential. Finally, several numerical experiments using Navier-Stokes flow illustrate the applicability of the method, for the localization of a bi-dimensional cardiac valve from MRI and ultrasound flow type imaging data.

中文翻译：

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基于内部速度测量的流动障碍物识别的分布式电阻反演方法

我们提出了一种用于 Oseen 方程修改版本的不可压缩流体流中障碍物识别的惩罚参数方法。所提出的方法包括向系统添加高阻力电位，使得其边界支持的某些子集代表障碍物。这允许在固定域中工作并通过一些合适的成本函数高度简化逆问题的解决方案。最小值和一阶和二阶最优条件的存在是通过 Oseen 方程的解相对于势能的可微性推导出来的。最后，几个使用 Navier-Stokes 流的数值实验说明了该方法的适用性，用于从 MRI 和超声流型成像数据定位二维心脏瓣膜。