Verification of higher-order discontinuous Galerkin method for hexahedral elements

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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.
Original languageUndefined
Pages (from-to)719-725
Number of pages7
JournalComptes rendus mécanique
Volume333
Issue number9
DOIs
Publication statusPublished - 2005

Keywords

  • Acoustics
  • Computational aeroacoustics
  • Finite Element Method
  • IR-54566
  • Hexahedral elements
  • METIS-228840
  • Discontinuous Galerkin method

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