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Spectral Difference Method for Unstructured Grids II: Extension to the Euler Equations

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An efficient, high-order, conservative method named the spectral difference method has been developed recently for conservation laws on unstructured grids. It combines the best features of structured and unstructured grid methods to achieve high-computational efficiency and geometric flexibility; it utilizes the concept of discontinuous and high-order local representations to achieve conservation and high accuracy; and it is based on the finite-difference formulation for simplicity. The method is easy to implement since it does not involve surface or volume integrals. Universal reconstructions are obtained by distributing solution and flux points in a geometrically similar manner for simplex cells. In this paper, the method is further extended to nonlinear systems of conservation laws, the Euler equations. Accuracy studies are performed to numerically verify the order of accuracy. In order to capture both smooth feature and discontinuities, monotonicity limiters are implemented, and tested for several problems in one and two dimensions. The method is more efficient than the discontinuous Galerkin and spectral volume methods for unstructured grids.

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Authors and Affiliations

  1. Department of Aerospace Engineering, Iowa State University, 2271 Howe Hall, Ames, IA, 50011, USA

    Z. J. Wang

  2. NASA Ames Research Center, Mail Stop T27B-1, Moffett Field, CA, 94035, USA

    Yen Liu

  3. Department of Aeronautics and Astronautics, Stanford University, Durand Building, 496 Lomita Mall, Stanford, CA, 94305-4035, USA

    Georg May & Antony Jameson

Authors
  1. Z. J. Wang
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  2. Yen Liu
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  3. Georg May
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  4. Antony Jameson
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Correspondence to Z. J. Wang.

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Wang, Z.J., Liu, Y., May, G. et al. Spectral Difference Method for Unstructured Grids II: Extension to the Euler Equations. J Sci Comput 32, 45–71 (2007). https://doi.org/10.1007/s10915-006-9113-9

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