The paper presents recent developments of a computational code for the numerical investigation of acoustic propagation. The code solves the three-dimensional linear Euler equations using a Discontinuous Galerkin (DG) method for the spatial discretization and an explicit high-order low-storage Runge-Kutta method for advancing the solution in time. Thanks to DG discretization, high-order accurate numerical solutions on arbitrary unstructured hybrid grids have been easily computed. The code has been parallelized using MPI and preliminary results on a small 10-processor Linux cluster seem very promising.
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References
1.
CockburnB.KarniadakisG. E., and ShuC.-W.The development of discontinuous Galerkin methods. In CockburnB.KarniadakisG. E., and ShuC.-W., editors, Discontinuous Galerkin Methods: Theory, Computation, and Applications, volume 11 of Lecture Notes in Computational Science and Engineering, pages 3–50. Springer-Verlag, 2000. Proceedings of the I-st DGM Symposium, May, Newport, USA, 1999.
2.
ArnoldD.N.BrezziF.CockburnB., and MariniL.D.Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal., 2002, 39:1749–1779.
3.
BassiF. and RebayS.A high order discontinuous Galerkin method for compressible turbulent flows. In CockburnB.KarniadakisG. E., and ShuC.-W., editors, Discontinuous Galerkin Methods: Theory, Computation, and Applications, volume 11 of Lecture Notes in Computational Science and Engineering, pages 77–88. Springer-Verlag, 2000. Proceedings of the I-st DGM Symposium, May, Newport, USA, 1999.
4.
AtkinsH. and LockardD.. An Application of the Quadrature Free Discontinuous Galerkin Method. Third Computational Aeroacoustics (CAA) Workshop on Benchmark Problems, 2000, NASA/CP 2000-209790.
5.
AtkinsH. and ShuC.Quadrature-Free Implementation of Discontinuous Galerkin Method for Hyperbolic Equation. AIAA Journal1997, 36(5):775–782.
6.
AtkinsH. and LockardD.A High-Order Method Using Unstructured Grids for the Aeroacoustic Analysis of Realistic Aircraft Configuration. AIAA Paper 99-1945, 1999.
7.
NarkD.M.. The Use of Staggered Schemes and an Absorbing Buffer Zone for Computational Aeroacoustics. ICASE/Larc Workshop on Benchmark Problems in Computational Aeroacoustics (CAA), 1995, NASA Conference Publication 3300: 233–244.
CoolsR.. An Encyclopaedia of Cubature Formulas. Journal of Complexity. accepted.
10.
KennedyA.CarpenterH., and LewisR.Low-Storage, Explicit Runge-Kutta Schemes for the Compressible Navier Stokes Equation. ICASE Report No. 99–22, 1999.
11.
JohnsonC.. Numerical solution of partial differential equations by the finite element method. Cambridge University Press, 1995.
12.
HuF.Q.. On Absorbing Boundary Condition for Linearized Euler Equation by a Perfectly Matched Layer. Journal of Computational Physics, 1996, 129:201–219.
13.
TamC.K.W. and WebbJ.C.Dispersion-Relation-Preserving Schemes for Computational Acoustics. Journal of Computational Physics, 1993, 107:262–281.
14.
Ta'asanS. and NarkD.M.An Absorbing Buffer Zone Technique for Acoustic Wave Propagation. AIAA Paper 95-0164, 1995.
15.
KarypisG. and KumarV.METIS, a software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices. Technical Report Version 4.0, University of Minnesota, Department of Computer Science/Army HPC Research Center, 1998.
16.
BalayS.GroppW.T.McInnesL.C., and SmithB.F.PETSc Users Manual Technical Report ANL-95/11-Revision 2.1.3, Argonne National Laboratory, 2002.
17.
BaggagA.AtkinsH., and KeyesD.Parallel Implementation of Discontinuous Galerkin Method. ICASE Report No. 99-35, 1999.
18.
ShiehC.M. and MorrisP.J.Three-Dimensional Calculations of Acoustic Scattering by a Sphere: A Parallel Implementation. Second Computational Aeroacoustics (CAA) Workshop on Benchmark Problems, 1997, NASA CP 3352.
19.
MorrisP.J.. Scattering of Sound by a Sphere: Category 1: Problems 3 and 4. Second Computational Aeroacoustics (CAA) Workshop on Benchmark Problems, 1997, NASA CP 3352.
20.
HuF.Q.. A Stable, Perfectly Matched Layer for Linearized Euler Equations in Unsplit Physical Variables. Journal of Computational Physics, 2001, 173:455–480.
21.
HuF.Q.. On Constructing Stable Perfectly Matched Layers as an Absorbing Boundary Condition for Euler Equations. 40th AIAA Aerospace Sciences Meeting and Exhibit, 2002. Reno, NV.
