Curved boundary treatments for the discontinuous galerkin method applied to aeroacoustic propagation

AIAA Journal

Volumn 48, Issue 2, 2010, Pages 479-489

  Toulorge, Thomas ^a   Desmet, Wim ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC SCATTERING PROBLEM; AEROACOUSTIC PROPAGATION; BOUNDARY TREATMENT; CURVED BOUNDARY; CURVED ELEMENTS; DISCONTINUOUS GALERKIN METHODS; FREEFORMS; HIGH ORDER; HIGH-LIFT AIRFOILS; HIGHER ORDER; LINEARIZED EULER EQUATION; REALISTIC GEOMETRY; SECOND ORDERS; STRAIGHT EDGE; TETRAHEDRAL ELEMENTS; UNSTRUCTURED GRID;

ACOUSTIC WAVE PROPAGATION; ACOUSTIC WAVE SCATTERING; AEROACOUSTICS; AIRFOILS; EULER EQUATIONS;

GALERKIN METHODS;

EID: 76949102764     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/1.45353     Document Type: Conference Paper

References (28)

1. Reed,W. H., and Hill, T. R., "Triangular Mesh Methods for the Neutron Transport Equation," Los Alamos Scientific Lab., Technical Rept. LAUR- 73-479, 1973.
2. Lesaint, P., and Raviart, P. A., "On a Finite Element Method for Solving the Neutron Transport Equation," Mathematical Aspects of Finite Element in Partial Differential Equations, Academic Press, New York, 1974.
3. Atkins, H., and Shu, C.-W., "Quadrature-Free Implementation of the Discontinuous Galerkin Method for Hyperbolic Equations," AIAA Journal, Vol.36, No.5, 1998, pp. 775-782. doi:10.2514/2.436
4. Hu, F. Q., and Atkins, H. L., "Two-Dimensional Wave Analysis of the Discontinuous Galerkin Method with Nonuniform Grids and Boundary Conditions," 8th AIAA/CEAS Aeroaoustic Conference, AIAA, Reston, VA, 2002.
5. Hu, F. Q., Hussaini, M. Y., and Rasetarinera, P., "An Analysis of the Discontinuous Galerkin Method for Wave Propagation Problems," Journal of Computational Physics, Vol.151, No.2, 1999, pp. 921-946. doi:10.1006/jcph. 1999.6227
6. Hagmeijer, R., Blom, C. P. A., and Hoeijmakers, H. W. M., "Wave- Speed Analysis of Discontinuous Galerkin Finite Element Method for Aeroacoustics," ECCOMAS Computational Fluid Dynamics Conference 2001, International Center for Numerical Methods in Engineering, Barcelona, Sept. 2001.
7. Ainsworth, M., Monk, P., and Muniz, W., "Dispersive and Dissipative Properties of Discontinuous Galerkin Finite Element Methods for the Second-Order Wave Equation," Journal of Scientific Computing, Vol.27, Nos. 1-3, 2006, pp. 5-40. doi:10.1007/s10915-005-9044-x (Pubitemid 43876927)
8. Chevaugeon, N., Remacle, J.-F., Gallez, X., Ploumhans, P., and Caro, S., "Efficient Discontinuous Galerkin Methods for Solving Acoustic Problems," 11th AIAA/CEAS Aeroacoustics Conference, AIAA, Reston, VA, Paper 2005-2823, 2005.
9. Chevaugeon, N., Hillewaert, K., Gallez, X., Ploumhans, P., and Remacle, J.-F., "Optimal Numerical Parameterization of Discontinuous Galerkin Method Applied to Wave Propagation Problems," Journal of Computational Physics, Vol.223, 2007, pp. 188-207. doi:10.1016/j.jcp.2006.09.005
10. Reymen, Y., Baelmans, M., and Desmet, W., "Study of Convergence and Efficiency of a Nodal Quadrature-Free Discontinuous Galerkin Method on Meshes of Tetrahedral and Hexahedral Elements," International Conference On Spectral and High Order Methods, Global Science Press, Hong Kong, 2007.
11. Reymen, Y., Baelmans, M., and Desmet, W., "On the Performance of the Quadrature-Free Discontinuous Galerkin Method on Hexahedral and Tetrahedral Grids for Linearized Euler Equations," 14th AIAA/ CEAS Aeroacoustics Conference, AIAA, Reton,VA, Paper 2008-3001, 2008.
12. Hesthaven, J. S., and Warburton, T., "Nodal High-Order Methods on Unstructured Grids," Journal of Computational Physics, Vol.181, 2002, pp. 186-221. doi:10.1006/jcph.2002.7118
13. Blom, C. P. A., "Discontinuous Galerkin Method on Tetrahedral Elements for Aeroacoustics," Ph.D. Thesis, Univ. of Twente, Enschede, The Netherlands, 2003.
14. Rao, P. P., "High Order Unstructured Grid Methods for Computational Aeroacoustics," Ph.D. Thesis, Pennsylvania State Univ., State College, PA, 2004.
15. Dumbser, M., and Munz, C.-D., "ADER Discontinuous Galerkin Schemes for Aeroacoustics," Comptes Rendus Mecanique, Vol.333, No.9, 2005, pp. 683-687. doi:10.1016/j.crme.2005.07.008 (Pubitemid 41492046)
16. Delorme, P., Mazet, P., Peyret, C., and Ventribout, Y., "Computational Aeroacoustics Applications Based on a Discontinuous Galerkin Method," Comptes Rendus Mecanique, Vol.333, No.9, 2005, pp. 676-682. doi:10.1016/j.crme.2005.07.007 (Pubitemid 41492045)
17. Bassi, F., and Rebay, S., "High-Order Accurate Discontinuous Finite Element Solution of the 2D Euler Equations," Journal of Computational Physics, Vol.138, No.2, 1997, pp. 251-285. doi:10.1006/jcph.1997.5454 (Pubitemid 127170411)
18. Krivodonova, L., and Berger, M., "High-Order Accurate Implementation of Solid Wall Boundary Conditions in Curved Geometries," Journal of Computational Physics, Vol.211, No.2, 2006, pp. 492-512. doi:10.1016/j.jcp.2005. 05.029 (Pubitemid 41472438)
19. Atkins, H. L., "Continued Development of the Discontinuous Galerkin Method for Computational Aeroacoustic Applications," AIAA, Reston, VA, Paper 97-1581, 1997.
20. Reymen, Y., "3D High-Order Discontinuous Galerkin Methods for Time-Domain Simulation of Flow Noise Propagation," Ph.D. Thesis, Katolieke Universiteit Leuven, 2008.
21. Carpenter, M. H., and Kennedy, C. A., "A Fourth-Order 2N-Storage Runge-Kutta Scheme," NASATM 109112, 1994.
22. Reymen, Y., Baelmans, M., and Desmet, W., "A 3D Discontinuous Galerkin Method for Aeroacoustic Propagation," 12th International Congress on Sound and Vibration, International Institute of Acoustics and Vibration, Lisbon, 2005.
23. Hesthaven, J. S., "From Electrostatics to Almost Optimal Nodal Sets for Polynomial Interpolation in a Simplex," SIAM Journal on Numerical Analysis, Vol.35, No.2, 1998, pp. 655-676. doi:10.1137/S003614299630587X
24. Geuzaine, C., and Remacle, J. F., "Gmsh: AThree-Dimensional Finite Element Mesh Generator with Built-In Pre- and Post-Processing Facilities," International Journal for Numerical Methods in Engineering, Vol.79, No.11, 2009, pp. 1309-1331.
25. Tam, C. K. W., and Hardin, J. C. (Eds.), "Second Computational AeroacousticsWorkshop on Benchmark Problems,"NASAPaper 3352, 1997.
26. Toulorge, T., Reymen, Y., and Desmet, W., "A 2D Discontinuous Galerkin Method for Aeroacoustics with Curved Boundary Treatment," Proceedings of the ISMA2008 Conference, Katholieke Universiteit Leuven, Leuven, Belgium, 2008, pp. 565-578.
27. Denia, F. D., Albelda, J., Fuenmayor, F. J., and Torregrosa, A. J., "Acoustic Behaviour of Elliptical Chamber Mufflers," Journal of Sound and Vibration, Vol.241, No.3, 2001, pp. 401-421. doi:10.1006/jsvi.2000.3289 (Pubitemid 32425151)
28. Hong, K., and Kim, J., "Natural Mode Analysis of Hollow and Annular Elliptical Cylindrical Cavities," Journal of Sound and Vibration, Vol.183, No.2, 1995, pp. 327-351. doi:10.1006/jsvi.1995.0257