Application of Discontinuous Galerkin spectral method on hexahedral elements for aeroacoustic

Nicolas Castel (1) , Gary Cohen (1) , Marc Duruflé (1, 2)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
2 IMB - Institut de Mathématiques de Bordeaux

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 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 3-D numericals experiments show the importance of penalization, and the advantage of using high order.

Domaines: Equations aux dérivées partielles [math.AP]

Nicolas Castel, Gary Cohen, Marc Duruflé. Application of Discontinuous Galerkin spectral method on hexahedral elements for aeroacoustic. Journal of Computational Acoustics, 2009, 17 (2), pp.175-196. ⟨hal-00403787⟩