APPLICATION OF DISCONTINUOUS GALERKIN SPECTRAL METHOD ON HEXAHEDRAL ELEMENTS FOR AEROACOUSTIC

Abstract

A discontinuous Galerkin method is developed for linear hyperbolic systems on general hexahedral meshes. The use of hexahedral elements and tensorized quadrature formulas to evaluate the integrals leads to an efficient matrix–vector product. It is shown that for high order approximations, the reduction in computational time can be very important, compared to tetrahedral elements. Two choices of quadrature points are considered, the Gauss points or Gauss–Lobatto points. The method is applied to the aeroacoustic system ("simplified" Linearized Euler Equations). Some 3D numerical experiments show the importance of penalization, and the advantage of using high order.