A variational approach to optical flow estimation of unsteady incompressible flows

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• 作者：Souvik Roy ; Praveen Chandrashekar…
• 关键词：Euler ; Navier–Stokes ; Vorticity ; Streamfunction ; Discontinuous Galerkin ; Optimization ; Linearization ; Helmholtz decomposition ; Incompressible
• 刊名：International Journal of Advances in Engineering Sciences and Applied Mathematics
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：7
• 期：3
• 页码：149-167
• 全文大小：2,866 KB
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  35.Roy, S., Chandrashekar, P., Vasudeva Murthy, A.S.: A variational approach to optical flow estimation of incompressible fluid flow. J. Comput. Vis. Sci. (2015, submitted)
  
• 作者单位：Souvik Roy (1)
  Praveen Chandrashekar (1)
  A. S. Vasudeva Murthy (1)
  
  1. TIFR Center for Applicable Mathematics, Bangalore, 560065, India
  
• 刊物类别：Engineering
• 刊物主题：Applied Mathematics and Computational Methods of Engineering
  
• 出版者：Springer India
• ISSN：0975-5616

文摘

We consider optical flow estimation of flows with vorticity governed by 2D incompressible Euler and Navier–Stokes equations . A vorticity-streamfunction formulation and optimization techniques are used. We use Helmholtz decomposition of the velocity field and prove existence of an unique velocity and vorticity field for the linearized vorticity equations. Discontinuous galerkin finite elements are used to solve the vorticity equation for Euler’s flow to efficiently track discontinuous vortices. Finally we test our method with two vortex flows governed by Euler and Navier–Stokes equations at high Reynolds number which support our theoretical results.