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Numerical Simulation of Compressible Flow Using Spectral Difference Method with Quadrilateral Elements

Kianvashrad, Nadia | 2011

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 42546 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Hejranfar, Kazem
  7. Abstract:
  8. In the present work, the numerical simulation of 2D inviscid compressible flows by using the spectral difference (SD) method on quadrilateral meshes is performed. The SD method combines the most desirable features of structured and unstructured grid methods to attain computational efficiency and geometric flexibility. Similar to the discontinuous Galerkin (DG) and spectral volume (SV) methods, the SD scheme utilizes the concept of discontinuous and high-order local representations to achieve conservation and high accuracy. The SD method is based on the finite-difference formulation and thus its formulation is simpler than the DG and SV methods because it does not involve test function or surface integral. In this method, two sets of structured points, namely “unknown points” and “flux points”, are defined in each cell to support the reconstruction of desirable order of accuracy. The differential form of the conservation laws is satisfied at nodal unknown points while the flux derivatives expressed in terms of values of flux points. For calculating the numerical flux at boundary flux points of each cell, an approximate Riemann solver such as the Rusanov scheme or the Roe scheme is used. In this study, the formulation of the SD method to calculated 2D inviscid compressible flows is described and the representative placements of unknown points and flux points for different orders of accuracy for quadrilateral elements are given in detail. The numerical solution of the 1D and 2D linear wave equation and also the 2D inviscid isentropic vortex is carried out by using the SD method. The computations are also performed by the upwind method and the results are compared with those of the SD method for different orders of accuracy. The effect of applying different numerical fluxes on the accuracy and efficiency of the SD method is also examined
  9. Keywords:
  10. Spectral Difference Method ; Compressible Flow ; Quadrilateral Elements

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