Level Set Projection Method for Incompressible Navier-Stokes on Arbitrary Boundaries

  • Bertrand Williams-Rioux

Student thesis: Master's Thesis


Second order level set projection method for incompressible Navier-Stokes equations is proposed to solve flow around arbitrary geometries. We used rectilinear grid with collocated cell centered velocity and pressure. An explicit Godunov procedure is used to address the nonlinear advection terms, and an implicit Crank-Nicholson method to update viscous effects. An approximate pressure projection is implemented at the end of the time stepping using multigrid as a conventional fast iterative method. The level set method developed by Osher and Sethian [17] is implemented to address real momentum and pressure boundary conditions by the advection of a distance function, as proposed by Aslam [3]. Numerical results for the Strouhal number and drag coefficients validated the model with good accuracy for flow over a cylinder in the parallel shedding regime (47 < Re < 180). Simulations for an array of cylinders and an oscillating cylinder were performed, with the latter demonstrating our methods ability to handle dynamic boundary conditions.
Date of AwardJan 12 2012
Original languageEnglish (US)
Awarding Institution
  • Biological, Environmental Sciences and Engineering
SupervisorRavi Samtaney (Supervisor)


  • level set
  • projection
  • incompressible
  • multigrid
  • navier-stokes

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