A variational approach to optical flow estimation of unsteady incompressible flows

  • Souvik Roy
  • Praveen Chandrashekar
  • A. S. Vasudeva Murthy


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.


Euler Navier–Stokes Vorticity Streamfunction Discontinuous Galerkin Optimization Linearization Helmholtz decomposition Incompressible 

Mathematics Subject Classification



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Copyright information

© Indian Institute of Technology Madras 2015

Authors and Affiliations

  • Souvik Roy
    • 1
  • Praveen Chandrashekar
    • 1
  • A. S. Vasudeva Murthy
    • 1
  1. 1.TIFR Center for Applicable MathematicsBangaloreIndia

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