A high-order immersed boundary method for acoustic wave scattering and low-Mach number flow-induced sound in complex geometries. (English) Zbl 1391.76698

Summary: A new sharp-interface immersed boundary method based approach for the computation of low-Mach number flow-induced sound around complex geometries is described. The underlying approach is based on a hydrodynamic/acoustic splitting technique where the incompressible flow is first computed using a second-order accurate immersed boundary solver. This is followed by the computation of sound using the linearized perturbed compressible equations (LPCE). The primary contribution of the current work is the development of a versatile, high-order accurate immersed boundary method for solving the LPCE in complex domains. This new method applies the boundary condition on the immersed boundary to a high-order by combining the ghost-cell approach with a weighted least-squares error method based on a high-order approximating polynomial. The method is validated for canonical acoustic wave scattering and flow-induced noise problems. Applications of this technique to relatively complex cases of practical interest are also presented.


76Q05 Hydro- and aero-acoustics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics
Full Text: DOI Link


[1] Stevens, K.N., Acoustic phonetics, (1998), The MIT Press Cambridge, Massachusetts, London, England
[2] Mittal, R.; Simmons, S.P.; Najjar, F., Numerical study of pulsatile flow in a constricted channel, J. fluid mech., 485, 337-378, (2003) · Zbl 1070.76060
[3] El-Seaier, M.; Lilja, O.; Lukkarinen, S.; Sörnmo, L.; Sepponen, R.; Pesonen, E., Computer-based detection and analysis of heart sound and murmur, Ann. biomed. eng., 33, 7, 937-942, (2005)
[4] Lehmann, J., Auscultation of heart sounds, Am. J. nursing, 72, 7, 1242-1246, (1972)
[5] Howe, M.S., On the hydroacoustics of a trailing edge with a detached flap, J. sound vib., 239, 4, 801-817, (2001)
[6] Bourgoyne, D.A.; Hamel, J.M.; Judge, C.Q.; Ceccio, S.L.; Dowling, D.R., Hydrofoil near-wake sound sources at high Reynolds number, J. acoust. soc. am., 111, 5, 2425, (2002)
[7] Howe, M.S., Sound produced by a vortex interacting with a cavitated wake, J. fluid mech., 543, 333-347, (2005) · Zbl 1080.76049
[8] Terai, T., On calculation of sound fields around three dimensional objects by integral equation methods, J. sound vib., 69, 1, 71-100, (1980) · Zbl 0435.76053
[9] Shen, L.; Liu, Y.J., An adaptive fast multipole boundary element method for three-dimensional acoustic wave problems based on the burton – miller formulation, Comput. mech., 40, 461-472, (2007) · Zbl 1176.76083
[10] Colonius, T.; Lele, S.K., Computational aeroacoustics: progress on nonlinear problems of sound generation, Prog. aerospace sci., 40, 6, 345-416, (2004)
[11] Bailly, C.; Bogey, C.; Marsden, O., Progress in direct noise computation, Int. J. aeroacoust., 9, 123-143, (2010)
[12] Lele, S.K., Compact finite difference schemes with spectral-like resolution, J. comput. phys., 103, 16-42, (1992) · Zbl 0759.65006
[13] Tam, C.K.W.; Webb, J.C., Dispersion – relation-preserving finite difference schemes for computational acoustics, J. comput. phys., 107, 262-281, (1993) · Zbl 0790.76057
[14] Sherer, S.E.; Scott, J.N., High-order compact finite difference methods on general overset grids, J. comput. phys., 210, 459-496, (2005) · Zbl 1113.76068
[15] S.E. Sherer, M.R. Visbal, High-order overset-grid simulations of acoustic scattering from multiple cylinders, in: Proceedings of the Fourth Computational Aeroacoustics (CAA) Workshop on Benchmark Problems, NASA/CP-2004-212954, 2004, pp. 255-266.
[16] Hu, F.Q.; Hussaini, M.Y.; Rasetarinera, P., An analysis of the discontinuous Galerkin for wave propagation problems, J. comput. phys., 151, 921-946, (1999) · Zbl 0933.65113
[17] Chevaugeon, N.; Hillewaert, K.; Gallez, X.; Ploumhans, P.; Remacle, J.-F., Optimal numerical parameterization of discontinuous Galerkin method applied to wave propagation problems, J. comput. phys., 223, 188-207, (2007) · Zbl 1113.65092
[18] Dumbser, M.; Munz, C.-D., ADER discontinuous Galerkin schemes for aeroacoustics, CR mecanique, 333, 683-687, (2005) · Zbl 1107.76044
[19] T. Toulorge, Y. Reymen, W. Desmet, A 2D discontinuous Galerkin method for aeroacoustics with curved boundary treatment, in: Proceedings of International Conference on Noise and Vibration Engineering (ISMA2008), 2008, pp. 565-578.
[20] Mittal, R.; Iaccarino, G., Immersed boundary methods, Annu. rev. fluid mech., 37, 239-261, (2005) · Zbl 1117.76049
[21] D. Casalino, P. Di Francescantonio, Y. Druon, GFD Predictions of Fan Noise Propagation, AIAA Paper, 2004-2989, 2004.
[22] R. Arina, B. Mohammadi, An Immersed Boundary Method for Aeroacoustics Problems, AIAA Paper, 2008-3003, 2008.
[23] M. Cand, 3-Dimensional Noise Propagation using a Cartesian Grid, AIAA Paper, 2004-2816, 2004.
[24] Liu, M.; Wu, K., Aerodynamic noise propagation simulation using immersed boundary method and finite volume optimized prefactored compact scheme, J. therm. sci., 17, 4, 361-367, (2008)
[25] Linnick, M.N.; Fasel, H.F., A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains, J. comput. phys., 204, 157-192, (2005) · Zbl 1143.76538
[26] de Tullio, M.D.; De Palma, P.; Iaccarino, G.; Pascazio, G.; Napolitano, M., An immersed boundary method for compressible flows using local grid refinement, J. comput. phys., 225, 2098-2117, (2007) · Zbl 1118.76043
[27] De Palma, P.; de Tullio, M.D.; Pascazio, G.; Napolitano, M., An immersed boundary method for compressible viscous flows, Comput. fluids, 35, 693-702, (2006) · Zbl 1177.76306
[28] Ghias, R.; Mittal, R.; Dong, H., A sharp interface immersed boundary method for compressible viscous flows, J. comput. phys., 225, 528-553, (2007) · Zbl 1343.76043
[29] Liu, Q.; Vasilyev, O.V., A Brinkman penalization method for compressible flows in complex geometries, J. comput. phys., 227, 946-966, (2007) · Zbl 1388.76259
[30] Hardin, J.C.; Pope, D.S., An acoustic/viscous splitting technique for computational aeroacoustics, Theoret. comput. fluid dyn., 6, 323-340, (1994) · Zbl 0822.76057
[31] Seo, J.H.; Moon, Y.J., The perturbed compressible equations for aeroacoustic noise prediction at low Mach numbers, Aiaa j., 43, 1716-1724, (2005)
[32] Seo, J.H.; Moon, Y.J., Linearized perturbed compressible equations for low Mach number aeroacoustics, J. comput. phys., 218, 702-719, (2006) · Zbl 1161.76546
[33] Mittal, R.; Dong, H.; Bozkurttas, M.; Najjar, F.M.; Vargas, A.; von Loebbecke, A., A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries, J. comput. phys., 227, 2852-4825, (2008) · Zbl 1388.76263
[34] Luo, H.; Mittal, R.; Zheng, X.; Bielamowicz, S.A.; Walsh, R.J.; Hahn, J.K., An immersed-boundary method for flow – structure interaction in biological systems with application to phonation, J. comput. phys., 227, 9303-9332, (2008) · Zbl 1148.74048
[35] Lighthill, M.J., On sound generated aerodynamically. I. general theory, Proc. royal soc. London, ser. A, 211, 564-587, (1952) · Zbl 0049.25905
[36] Seo, J.H.; Moon, Y.J., Aerodynamic noise prediction for long-span bodies, J. sound vib., 306, 564-579, (2007)
[37] Moon, Y.J.; Seo, J.H.; Bae, Y.M.; Roger, M.; Becker, S., A hybrid prediction for low-subsonic turbulent flow noise, Comput. fluids, 39, 1125-1135, (2010) · Zbl 1242.76079
[38] Goldstein, M.E., A generalized acoustic analogy, J. fluid mech., 488, (2004) · Zbl 1063.76630
[39] Chorin, A.J., On the convergence of discrete approximations to the navier – stokes equations, Math. comput., 23, 106, 341-353, (1969) · Zbl 0184.20103
[40] Jameson, A., Numerical solution of the Euler equations for compressible inviscid fluids, (), 199-245
[41] Gaitonde, D.; Shang, J.S.; Young, J.L., Practical aspects of higher-order accurate finite volume schemes for wave propagation phenomena, Int. J. numer. method eng., 45, 1849-1869, (1999) · Zbl 0959.65103
[42] Visbal, M.R.; Gaitonde, D.V., High-order accurate methods for complex unsteady subsonic flows, Aiaa j., 37, 10, 1231-1239, (1999)
[43] Carnahan, B.; Luther, H.A.; James, O.W., Applied numerical methods, (1969), Wiley New York · Zbl 0195.44701
[44] Li, Z., A fast interactive algorithm for elliptic interface problems, SIAM J. numer. anal., 35, 1, 230-254, (1998) · Zbl 0915.65121
[45] Press, W.H.; Teukolsky, S.A.; Vetterling, W.T.; Flannery, B.P., Numerical recipes: the art of scientific computing, (2007), Cambridge Univ. Press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo · Zbl 1132.65001
[46] D.V. Gaitonde, M.R. Visbal, Further Development of a Navier-Stokes Solution Procedure Based on Higher-Order Formulations, Technical Paper 99-0557, AIAA Press, Washington, DC, 1999.
[47] Visbal, M.R.; Gaitonde, D.V., On the use of higher-order finite-difference schemes on curvilinear and deforming meshes, J. comput. phys., 181, 155-185, (2002) · Zbl 1008.65062
[48] N.B. Edgar, M.R. Visbal, A General Buffer Zone Type Non-reflecting Boundary Condition for Computational Aeroacoustics, AIAA Paper 2003-3300, 2003.
[49] C.K.W. Tam, J.C. Hardin (Eds.), Second Computational Aeroacoustics (CAA) Workshop on Benchmark Problems, NASA-CP-3352, 1997.
[50] Sherer, S.E., Scattering of sound from axisymmetric sources by multiple circular cylinders, J. acoust. soc. am., 115, 488-496, (2004)
[51] Morris, P.J., Scattering of sound from a spatially distributed, spherically symmetric source by a sphere, J. acoust. soc. am., 98, 3536-3539, (1995)
[52] Williamson, C.H.K., Vortex dynamics in the cylinder wake, Annu. rev. fluid mech., 28, 477-539, (1996) · Zbl 0899.76129
[53] Henderson, R.D., Detail of the drag curve near the onset of vortex shedding, Phys. fluids, 7, 2102-2104, (1995)
[54] Titze, I.R., Principles of voice production, (1994), Prentice Hall
[55] Zhao, W.; Zhang, C.; Frankel, S.H.; Mongeau, L., Computational aeroacoustics of phonation, part I: computational methods and sound generation mechanism, J. acou. soc. am., 112, 2134-2146, (2002)
[56] Bae, Y.; Moon, Y.J., Computation of phonation aeroacoustics by an INS/PCE splitting method, Comput. fluids, 37, 1332-1343, (2008) · Zbl 1237.76164
[57] Link, G.; Kaltenbacher, M.; Breuer, M.; Dollinger, M., A 2D finite-element scheme for fluid – solid-acoustic interaction and its application to human phonation, Comput. methods appl. mech. eng., 198, 3321-3334, (2009) · Zbl 1230.74188
[58] Zheng, X.; Bielamowicz, S.; Luo, H.; Mittal, R., A computational study of the effect of false vocal folds on glottal flow and vocal fold vibration during phonation, Ann. biomed. eng., 37, 625-642, (2009)
[59] Fant, G., Glottal flow: models and interaction, J. phonet., 14, 393-399, (1986)
[60] Plumpe, M.D.; Quatieri, T.F.; Reynolds, D.A., Modeling of the glottal flow derivative waveform with application to speaker identification, IEEE trans. speech audio proc., 7, 5, 569-586, (1999)
[61] Stone, M., Imaging the tongue and vocal tract, J. disorder commun., 26, 11-23, (1991)
[62] Guerin, S.; Thomy, E.; Wright, M.C.M., Aeroacoustics of automotive vents, J. sound vib., 285, 859-875, (2005)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.