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Development of an Incompressible Smoothed Particle Hydrodynamics Method based on Vorticity-stream Function Formulation

Alibakhshian, Mohammad Reza | 2017

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 50120 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Hejranfar, Kazem
  7. Abstract:
  8. In the present study, an incompressible smoothed particle hydrodynamics method based on vorticity-stream function (VSF-SPH) formulation is developed and assessed for simulating steady and unsteady incompressible flows. The vorticity-stream function formulation in the Eulerian reference frame is written in a Lagrangian reference frame to provide an appropriate incompressible SPH algorithm. The advantage of the proposed smoothed particle hydrodynamics method based on the vorticity-stream function (VSF-SPH) formulation over the weakly compressible SPH (WCSPH) is that the VSF-SPH method is a truly incompressible SPH algorithm and it does not involve any approximate enforcement of the incompressibility condition that may cause to use a large magnitude speed of sound implying a small time step in the simulations. The approximate enforcement of the incompressibility condition used in the WCSPH method also causes spurious oscillations in the density and pressure fields which is not the case for the VSF-SPH formulation. The accuracy and robustness of the proposed SPH method (VSF-SPH) are demonstrated by solving different 2D incompressible flow problems. A sensitivity study is also conducted to evaluate the effects of particle resolution and the value of smoothing length on the accuracy and convergence rate of the solution. To validate the results, different 2D test cases are considered herein that are the Green-Taylor vortices, the Couette flow and the flow in a lid-driven cavity. Results obtained for these test cases are in good agreement with the available analytical and numerical results. The study shows the proposed incompressible smoothed particle hydrodynamics method based on vorticity-stream function (VSF-SPH) formulation is accurate and robust for simulating 2D steady and unsteady incompressible flow problems
  9. Keywords:
  10. Smoothed Particle Hydrodynamics (SPH) ; Incompressible Flow ; Vorticity-Stream Function (VSF) Formulation

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