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Wave Computation Using a A High Order Space-time Riemann Solver Free Method

Shuangzhang Tu, Qing Pang, Haibin Xiang
2011 17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference)   unpublished
This paper aims to demonstrate the accuracy and effectiveness of a new implementation of the high-order space-time discontinuous Galerkin cell vertex scheme (DG-CVS) in solving problems involving wave propagation. The new implementation employs the conservative variables as the working variables and the Cauchy-Kovalewski procedure is used to obtain the expansions of the flux vectors in terms of the basis polynomials to facilitate the quadrature-free implementation. Particularly, it will be
more » ... ly, it will be shown that DG-CVS handles very well the nonreflecting boundary conditions (NRBC) using a much simpler approach than traditional approaches. In the current approach, the outmost layer of cells in the computational domain are considered as ghost cells if NRBC is needed there. The solutions at the ghost cells are not computed using the DG-CVS formulation. Instead, they are copied from the adjacent interior locations at the previous half time level. Numerical results including a vortex advection, a 2-D shocktube problem and an acoustic propagation problem demonstrate that the new implementation of DG-CVS is accurate in solving the compressible Euler equations and is strikingly effective in dealing with the nonreflecting boundary conditions.
doi:10.2514/6.2011-2846 fatcat:5ldwefgy7vgzfkinh4emvck25i