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Numerical Simulation of 2D Inviscid Compressible Magnetohydrodynamic Flows by Spectal Difference Method

Kharratyan, Mahdi | 2009

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 39488 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Hejranfar, Kazem
  7. Abstract:
  8. In the present study, the numerical solution of 2D inviscid compressible ideal magnetohydrodynamic (MHD) flows by using the spectral difference (SD) method on unstructured meshes is performed. The SD method combines the most desirable features of structured and unstructured grid methods to have computational efficiency and geometric flexibility to accurately compute flow over complex geometries. In the SD method, two sets of structured points, namely “unknown points” and “flux points”, are defined in each cell to support the reconstruction of given 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. To calculate the numerical flux at boundary flux points of each cell, approximate Riemann solvers such as the Rusanov scheme can be used. At first, the formulation of the SD method to compute 2D inviscid compressible flows is described and the representative placements of unknown and flux points with various orders of accuracy for triangular elements are given in detail. Then, the numerical solution procedure of the MHD equations using the SD method is described. The detailed formulation of the algorithm that uses the Roe scheme for calculating the numerical flux at flux points are is presented. The numerical solution of the wave equation and the 2D inviscid compressible flow over an airfoil at different conditions is carried out by the SD method. The 2D inviscid compressible MHD flow over a wedge is then computed and the effect of ionized flow on the flow filed characteristics is studied. The influence of applying different numerical fluxes on the accuracy and efficiency of the SD method is also examined
  9. Keywords:
  10. Plasma ; Magnetohydrodynamic Power Plant ; Spectral Difference Method ; Unknown Points ; Flux Points

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