×

zbMATH — the first resource for mathematics

A family of low dispersive and low dissipative explicit schemes for flow and noise computations. (English) Zbl 1042.76044
Summary: Explicit numerical methods for spatial derivation, filtering and time integration are proposed. They are developed with the aim of computing flow and noise with high accuracy and fidelity. All the methods are constructed in the same way by minimizing the dispersion and the dissipation errors in the wavenumber space up to \(k\varDelta x=\pi/2\) corresponding to four points per wavelength. They are shown to be more accurate, and also more efficient numerically, than most of the standard explicit high-order methods, for uniform and slowly non-uniform grids. Two problems involving long-range sound propagation are resolved to illustrate their respective precisions. Remarks about their practical applications are then made, especially about the connection with the boundary conditions. Finally, their relevance for the simulation of turbulent flows is emphasized.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76Q05 Hydro- and aero-acoustics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Tam, C.K.W., Computational aeroacoustics: issues and methods, Aiaa j., 33, 10, 1788, (1995) · Zbl 0856.76080
[2] Tam, C.K.W.; Webb, J.C., Dispersion-relation-preserving finite difference schemes for computational acoustics, J. comput. phys., 107, 262, (1993) · Zbl 0790.76057
[3] Lele, S.K., Compact finite difference schemes with spectral-like resolution, J. comput. phys., 103, 1, 16, (1992) · Zbl 0759.65006
[4] Haras, Z.; Ta’asan, S., Finite difference schemes for long-time integration, J. comput. phys., 114, 265, (1994) · Zbl 0808.65083
[5] Kim, J.W.; Lee, D.J., Optimized compact schemes with maximum resolution, Aiaa j., 34, 5, 887, (1996) · Zbl 0900.76317
[6] Mahesh, K., A family of high order finite difference schemes with good spectral resolution, J. comput. phys., 145, 332, (1998) · Zbl 0926.76081
[7] Hixon, R., Prefactored small-stencil compact schemes, J. comput. phys., 165, 2, 522, (2000) · Zbl 0990.76059
[8] Lockard, D.P.; Brentner, K.S.; Atkins, H.L., High-accuracy algorithms for computational aeroacoustics, Aiaa j., 33, 2, 246, (1995) · Zbl 0825.76490
[9] Tam, C.K.W.; Webb, J.C.; Dong, Z., A study of the short wave components in computational acoustics, J. comput. ac., 1, 1, 1, (1993) · Zbl 1360.76303
[10] C.K.W. Tam, H. Shen, Direct computation of nonlinear acoustic pulses using high order finite difference schemes, AIAA Paper 93-4325, 1993
[11] Visbal, M.R.; Gaitonde, D.V., High-order-accurate methods for complex unsteady subsonic flows, Aiaa j., 37, 10, 1231, (1999)
[12] Zingg, D.W.; Lomax, H.; Jurgens, H., High-accuracy finite-difference schemes for linear wave propagation, SIAM J. sci. comput., 17, 2, 328, (1996) · Zbl 0877.65063
[13] Hu, F.Q.; Hussaini, M.Y.; Manthey, J.L., Low-dissipation and low-dispersion runge – kutta schemes for computational acoustics, J. comput. phys., 124, 177, (1996) · Zbl 0849.76046
[14] Stanescu, D.; Habashi, W.G., 2N-storage low dissipation and dispersion runge – kutta schemes for computational acoustics, J. comput. phys., 143, 674, (1998) · Zbl 0952.76063
[15] Hixon, R.; Turkel, E., Compact implicit maccormack-type schemes with high accuracy, J. comput. phys., 158, 1, 51, (2000) · Zbl 0958.76059
[16] Bogey, C.; Bailly, C.; Juvé, D., Numerical simulation of the sound generated by vortex pairing in a mixing layer, Aiaa j., 38, 12, 2210, (2000)
[17] Bogey, C.; Bailly, C.; Juvé, D., Noise investigation of a high subsonic, moderate Reynolds number jet using a compressible LES, Theoret. comput. fluid dyn., 16, 4, 273, (2003) · Zbl 1051.76064
[18] Lesieur, M.; Métais, O., New trends in large-eddy simulations of turbulence, Annu. rev. fluid mech., 28, 45, (1996)
[19] Vasilyev, O.V.; Lund, T.S.; Moin, P., A general class of commutative filters for LES in complex geometry, J. comput. phys., 146, 82, (1998) · Zbl 0913.76072
[20] Germano, M.; Piomelli, U.; Moin, P.; Cabot, W.H., A dynamic subgrid-scale eddy viscosity model, Phys. fluids A, 3, 7, 1760, (1991) · Zbl 0825.76334
[21] Ghosal, S., An analysis of numerical errors in large-eddy simulations of turbulence, J. comput. phys., 125, 187, (1996) · Zbl 0848.76043
[22] Kravchenko, A.G.; Moin, P., On the effect of numerical errors in large eddy simulations of turbulent flows, J. comput. phys., 131, 310, (1997) · Zbl 0872.76074
[23] A. Jameson, W. Schmidt, E. Turkel, Numerical solution of the Euler equations by finite volume methods using Runge-Kutta time stepping schemes, AIAA Paper 81-1259, 1981
[24] Kennedy, C.A.; Carpenter, M.H., Several new numerical methods for compressible shear-layer simulations, Appl. numer. math., 14, 2, 397, (1994) · Zbl 0804.76062
[25] M.H. Carpenter, C.A. Kennedy, A fourth-order 2N storage Runge-Kutta scheme, NASA TM-109112, 1994
[26] Williamson, J.H., Low-storage runge – kutta schemes, J. comput. phys., 35, 48, (1980) · Zbl 0425.65038
[27] Tam, C.K.W.; Dong, Z., Wall boundary conditions for high-order finite-difference schemes in computational aeroacoustics, Theoret. comput. fluid dyn., 6, 303, (1994) · Zbl 0820.76061
[28] X. Gloerfelt, C. Bogey, C. Bailly, D. Juvé, Aerodynamic noise induced by laminar and turbulent boundary layers over rectangular cavities, AIAA Paper 2002-2476, 2002 (see also AIAA Paper 2003-3234, 2003)
[29] Tam, C.K.W.; Dong, Z., Radiation and outflow boundary conditions for direct computation of acoustic and flow disturbances in a nonuniform Mean flow, J. comput. ac., 4, 2, 175, (1996)
[30] Bogey, C.; Bailly, C., Three-dimensional non reflective boundary conditions for acoustic simulations: far-field formulation and validation test cases, Acta acoustica, 88, 4, 463, (2002)
[31] C. Bogey, C. Bailly, Direct computation of the sound radiated by a high Reynolds number, subsonic round jet, in: CEAS Workshop From CFD to CAA, Athens, Greece, November 7-8, 2002 (see also AIAA Paper 2003-3170, 2003)
[32] C. Bogey, C. Bailly, LES of a high Reynolds, high subsonic jet: effects of the subgrid modellings on flow and noise, AIAA Paper 2003-3557, 2003
[33] Visbal, M.R.; Rizzetta, D.P., Large-eddy simulation on curvilinear grids using compact differencing and filtering schemes, J. fluid engrg., 124, 836, (2002)
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.