Numerical Simulation of Compressible Magnetohydrodynamic Flow Using Spectral Difference Method on Quadrilateral Grids

Kafian, Hesam | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 49157 (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 solution of 2D inviscid compressible Magneto-hydrodynamic flow is performed by using the spectral difference (SD) method on quadrilateral grids. In this numerical method, similar to the discontinuous Galerkin (DG) and spectral volume (SV) methods, the concept of the discontinuous and high-order local representations is used to achieve conservation property and high-order accuracy. In the SD method, the test function or the surface integral is not involved and thus it has a simpler formulation than the DG and SV methods. In this numerical 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 the nodal unknown points while the flux derivatives expressed in terms of values of flux points. Two approximate Riemann solvers, namely, the Rusanov and Roe schemes are used for calculating the numerical flux at the boundary flux points of each cell. In the present study, the formulation of the SD method to compute the 2D inviscid compressible magneto-hydrodynamic flow on the quadrilateral elements is given and the numerical simulation of magneto-hydrodynamic problems is performed by applying this high-order accurate numerical method. The effect of applying the numerical flux on the accuracy and robustness of the SD method is also investigated
  9. Keywords:
  10. Quadrilateral Elements ; Spectral Difference Method ; Magnetohydrodynamic ; Compressible Flow ; Numerical Simulation

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