×

Development of PML absorbing boundary conditions for computational aeroacoustics: a progress review. (English) Zbl 1237.76119

Summary: Recent advances in the development of perfectly matched layer (PML) as absorbing boundary conditions for computational aeroacoustics are reviewed. The PML methodology is presented as a complex change of variables. In this context, the importance of a proper space-time transformation in the PML technique for Euler equations is emphasized. A unified approach for the derivation of PML equations is offered that involves three essential steps. The three-step approach is illustrated in details for the PML of linear and non-linear Euler equations. Numerical examples are also given that include non-reflecting boundary conditions for a ducted channel flow and mixing layer roll-up vortices.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76Q05 Hydro- and aero-acoustics
Full Text: DOI

References:

[1] Abarbanel, S.; Gottlieb, D., A mathematical analysis of the PML method, J Comput Phys, 134, 357 (1997) · Zbl 0887.65122
[2] Bayliss, A.; Turkel, E., Radiation boundary conditions for wave-like equations, Commun on Pure Appl Math, 33, 708-725 (1980) · Zbl 0438.35043
[3] Becache, E.; Bonnet-Ben Dhia, A.-S.; Legendre, G., Perfectly matched layers for the convected Helmholtz equation, SIAM J Numer Anal, 42, 1, 409-433 (2004) · Zbl 1089.76045
[4] Becache, E.; Fauqueux, S.; Joly, P., Stability of perfectly matched layers, group velocities and anisotropic waves, J Comput Phys, 188, 399-433 (2003) · Zbl 1127.74335
[5] Berenger, J. P., A perfectly matched layer for the absorption of electromagnetic waves, J Comput Phys, 114, 185-200 (1994) · Zbl 0814.65129
[6] Bodony, D. J., Analysis of sponge zones for computational fluid mechanics, J Comp Phys, 212, 681-702 (2006) · Zbl 1161.76539
[7] Chew, W. C.; Weedon, W. H., A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates, IEEE Microwave Opt Technol Lett, 7, 599-604 (1994)
[8] Collino, F.; Monk, P., The perfectly matched layer in curvilinear coordinates, SIAM J Sci Comp, 19, 6, 2016 (1998) · Zbl 0964.78018
[9] Dahl MD. Fourth Computational Aeroacoustics (CAA) Workshop on Benchmark Problems. NASA CP-2004-212954, 2004.; Dahl MD. Fourth Computational Aeroacoustics (CAA) Workshop on Benchmark Problems. NASA CP-2004-212954, 2004.
[10] Gedney, S. D., An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices, IEEE Trans Antennas Propagation, 44, 1630 (1996)
[11] Giles, M. B., Non-reflecting boundary conditions for Euler equation calculations, AIAA J, 28, 2050-2058 (1990)
[12] Hagstrom T, Nazarov I. Absorbing layers and radiation boundary conditions for jet flow simulations. AIAA paper 2002-2606, 2002.; Hagstrom T, Nazarov I. Absorbing layers and radiation boundary conditions for jet flow simulations. AIAA paper 2002-2606, 2002.
[13] Hagstrom T, Nazarov I. Perfectly matched layers and radiation boundary conditions for shear flow calculations. AIAA paper 2003-3298, 2003.; Hagstrom T, Nazarov I. Perfectly matched layers and radiation boundary conditions for shear flow calculations. AIAA paper 2003-3298, 2003.
[14] Hagstrom T, Goodrich J, Nazarov I, Dodson C. High-order methods and boundary conditions for simulating subsonic flows AIAA paper 2005-2869, 2005.; Hagstrom T, Goodrich J, Nazarov I, Dodson C. High-order methods and boundary conditions for simulating subsonic flows AIAA paper 2005-2869, 2005.
[15] Hayder, M. E.; Atkins, H. L., (Geers, T. L., Experiences with PML boundary conditions in fluid-flow computations, IUTAM symposium of computational methods for unbounded domains (1998), Kluwer Academic Publishers), 207-216 · Zbl 0955.76549
[16] Hu, F. Q., On absorbing boundary conditions of linearized Euler equations by a perfectly matched layer, J Comput Phys, 129, 201-219 (1996) · Zbl 0879.76084
[17] Hu FQ. On perfectly matched layer as an absorbing boundary condition. AIAA paper 96-1664, 1996.; Hu FQ. On perfectly matched layer as an absorbing boundary condition. AIAA paper 96-1664, 1996.
[18] Hu, F. Q., A stable, perfectly matched layer for linearized Euler equations in unsplit physical variables, J Comput Phys, 173, 455-480 (2001) · Zbl 1051.76593
[19] Hu, F. Q., Absorbing boundary conditions (a review), Int J Comput Fluid Dyn, 18, 6, 513-522 (2004) · Zbl 1065.76593
[20] Hu, F. Q., A perfectly matched layer absorbing boundary condition for linearized Euler equations with a non-uniform mean-flow, J Comput Phys, 208, 469-492 (2005) · Zbl 1329.76260
[21] Hu FQ. On the construction of PML absorbing boundary condition for the non-linear Euler equations. AIAA paper 2006-0798, 2006.; Hu FQ. On the construction of PML absorbing boundary condition for the non-linear Euler equations. AIAA paper 2006-0798, 2006.
[22] Hu, F. Q.; Hussaini, M. Y.; Manthey, J. L., Low-dissipation and -dispersion Runge-Kutta schemes for computational acoustics, J Comput Phys, 124, 177-191 (1996) · Zbl 0849.76046
[23] Mack, L. M., On the invicid acoustic-mode instability of supersonic shear flows, Theoret Comput Fluid Dyn, 2, 97-123 (1990) · Zbl 0722.76074
[24] Nataf, F., A new approach to perfectly matched layers for the linearized Euler system, J Comput Phys, 214, 2, 757-772 (2006) · Zbl 1088.76052
[25] Poinsot, T.; Lele, S. K., Boundary conditions for direct simulation of compressible viscous flows, J Comput Phys, 101, 104-129 (1992) · Zbl 0766.76084
[26] Tam, C. K.W.; Auriault, L.; Cambulli, F., Perfectly matched layer as an absorbing boundary condition for the linearized Euler equations in open and ducted domains, J Comput Phys, 144, 213-234 (1998) · Zbl 1392.76054
[27] Tam, C. K.W.; Hu, F. Q., On the three families of instability waves of high-speed jets, J Fluid Mech, 201, 447-483 (1989) · Zbl 0672.76054
[28] Tam, C. K.W.; Webb, J. C., Dispersion-relation-preserving schemes for computational acoustics, J Comput Phys, 107, 262-281 (1993) · Zbl 0790.76057
[29] Thompson, K. W., Time-dependent boundary conditions for hyperbolic systems, J Comput Phys, 68, 1-24 (1987) · Zbl 0619.76089
[30] Turkel, E.; Yefet, A., Absorbing PML boundary layers for wave-like equations, Appl Numer Math, 27, 533-557 (1998) · Zbl 0933.35188
[31] Zhao, L.; Cangellaris, A. C., GT-PML: generalized theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference time-domain grids, IEEE Trans Microwave Theory Tech, 44, 2555-2563 (1996)
[32] Whitman, G. B., Linear and nonlinear waves (1978), Willey
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.