A variational approach to estimate incompressible fluid flows

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• 作者：PRAVEEN CHANDRASHEKAR ; SOUVIK ROY…
• 关键词：Variational ; incompressible ; finite element ; optical flow ; Stokes ; Navier–Stokes
• 刊名：Proceedings - Mathematical Sciences
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：127
• 期：1
• 页码：175-201
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer India
• ISSN：0973-7685
• 卷排序：127

文摘

A variational approach is used to recover fluid motion governed by Stokes and Navier–Stokes equations. Unlike previous approaches where optical flow method is used to track rigid body motion, this new framework aims at investigating incompressible flows using optical flow techniques. We formulate a minimization problem and determine conditions under which unique solution exists. Numerical results using finite element method not only support theoretical results but also show that Stokes flow forced by a potential are recovered almost exactly.