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Numerical Solution of 2D Incompressible Flow Using Spectral Difference Method

Baradaran Kazemian, Behzad | 2015

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 48232 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Hejranfar, Kazem
  7. Abstract:
  8. In this study, an accurate numerical solution of the two-dimensional incompressible viscous flows is performed by using the spectral difference method on structured grids. The system of equations to be solved here is the preconditioned incompressible Navier-Stokes equations in the primitive variable formulation with the artificial compressibility approach. In the spectral difference method, two sets of the structured points, namely, “solution points” and “flux points” are defined in each cell for supporting the reconstruction of desirable order of accuracy. Here, the formulation of the spectral difference method is derived and the representative form of the solution and flux points for various orders of accuracy are given in detail. The differential form of the conservation laws is satisfied at the solution points and the flux derivatives are expressed in terms of the values of flux points. The Roe scheme is applied for the calculation of the numerical inviscid fluxes at the boundary flux points of each cell and the calculation of the numerical viscous fluxes is performed by an averaging technique. For time accurate solutions, the implicit dual-time stepping scheme is implemented. The numerical solution of the unsteady Couette flow, the unsteady Taylor vortex problem and the steady-state cavity flow is carried out using the spectral method and the results obtained are compared with the analytical and available numerical results. The study shows that the spectral difference method applied to solve the preconditioned incompressible Navier-Stokes equations, can accurately compute two-dimensional steady and unsteady viscous incompressible flows
  9. Keywords:
  10. Incompressible Viscous Flow ; Structured Grid ; Spectral Difference Method ; Artificial Compressibity Method ; Preconditioning

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