Verification of higher-order discontinuous Galerkin method for hexahedral elements |
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Authors: | Hüseyin Özdemir Rob Hagmeijer Hendrik Willem Marie Hoeijmakers |
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Institution: | Department of Mechanical Engineering, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands |
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Abstract: | A high-order implementation of the Discontinuous Galerkin (dg) method is presented for solving the three-dimensional Linearized Euler Equations on an unstructured hexahedral grid. The method is based on a quadrature free implementation and the high-order accuracy is obtained by employing higher-degree polynomials as basis functions. The present implementation is up to fourth-order accurate in space. For the time discretization a four-stage Runge–Kutta scheme is used which is fourth-order accurate. Non-reflecting boundary conditions are implemented at the boundaries of the computational domain.The method is verified for the case of the convection of a 1D compact acoustic disturbance. The numerical results show that the rate of convergence of the method is of order in the mesh size, with p the order of the basis functions. This observation is in agreement with analysis presented in the literature. To cite this article: H. Özdemir et al., C. R. Mecanique 333 (2005). |
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Keywords: | Acoustics Computational aeroacoustics Discontinuous Galerkin method Finite element method Hexahedral elements Acoustique Aéroacoustique numérique Méthode de Galerkine discontinue Méthode des éléments finis Éléments hexaédriques |
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