Verification of higher-order discontinuous Galerkin method for hexahedral elements


Özdemir, Hüseyin and Hagmeijer, Rob and Hoeijmakers, Hendrik Willem Marie (2005) Verification of higher-order discontinuous Galerkin method for hexahedral elements. Comptes Rendus. Mécanique, 333 (9). pp. 719-725. ISSN 1631-0721

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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 p+1 in the mesh size, with p the order of the basis functions. This observation is in agreement with analysis presented in the literature.
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Copyright:© 2005 Académie des Sciences
Engineering Technology (CTW)
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