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CABARET scheme with conservation-flux asynchronous time-stepping for nonlinear aeroacoustics problems. (English) Zbl 1349.76530

Summary: Explicit time stepping renders many high-resolution computational schemes to become less efficient when dealing with non-uniform grids typical of many aeroacoustic applications. Asynchronous time stepping, i. e., updating the solution in different cell sizes according to their local rates, is known to be a promising way to improve the efficiency of explicit time-stepping methods without compromise in accuracy. In the present paper, a new asynchronous time-stepping algorithm is developed for the Compact Accurately Boundary-Adjusting high-REsolution Technique (CABARET) Euler method. This allows to significantly speedup the original single-step CABARET method with non-uniform grids and improves its accuracy at the same time. Numerical examples are provided and issues associated with the method performance on various grid resolutions are discussed.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76F65 Direct numerical and large eddy simulation of turbulence
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76Q05 Hydro- and aero-acoustics
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[1] Wolf, W.; Lele, S., Trailing edge noise prediction using compressible LES and acoustics analogy, (17th AIAA/CEAS Aeroacoustics Conference, 32nd AIAA Aeroacoustics Conference. 17th AIAA/CEAS Aeroacoustics Conference, 32nd AIAA Aeroacoustics Conference, Portland, Oregon (5-8 June 2011))
[2] Men’shov, I.; Nakamura, Y., Hybrid explicit-implicit, unconditionally stable scheme for unsteady compressible flows, AIAA Journal, 42, 3, 551-559 (2004)
[3] Dawson, C.; Kirby, R., High resolution schemes for conservation laws with locally varying time steps, SIAM Journal on Scientific Computing, 22, 6, 2256 (2001) · Zbl 0980.35015
[4] Omelechenko, Y. A.; Karimabadi, H., Self-adaptive time integration of flux-conservative equations with sources, Journal of Computational Physics, 216, 179-194 (2006) · Zbl 1093.65083
[5] Omelechenko, Y. A.; Karimabadi, H., A time-accurate explicit multi-scale technique for gas dynamics, Journal of Computational Physics, 226, 282-300 (2007) · Zbl 1262.76079
[6] Tam, C. K.W.; Kurbatskii, K. A., Multi-size-mesh multi-time-step dispersion-relation-preserving scheme for multiple-scales aeroacoustics problems, International Journal of Computational Fluid Dynamics, 17, 2, 119-132 (2003) · Zbl 1115.76376
[7] Chang, S. C.; Wu, Y.; Yang, V.; Wang, X. Y., Local time-stepping procedures for the space-time conservation element and solution element method, International Journal of Computational Fluid Dynamics, 19, 5, 359-380 (July 2005)
[8] Goloviznin, V. M.; Samarskii, A. A., Difference approximation of convective transport with spatial splitting of time derivative, Mathematical Modelling, 10, 1, 86-100 (1998) · Zbl 1189.76364
[9] Karabasov, S. A.; Goloviznin, V. M., New efficient high-resolution method for nonlinear problems in aeroacoustics, AIAA Journal, 45, 12 (2007)
[10] Iserles, A., Generalized Leapfrog methods, IMA Journal of Numerical Analysis, 6, 3 (1986) · Zbl 0637.65089
[11] Roe, P. L., Linear bicharacteristic scheme without dissipation, SIAM Journal on Scientific Computing, 19, 1405-1427 (1998) · Zbl 0915.65106
[12] Karabasov, S. A.; Goloviznin, V. M., Compact accurately boundary adjusting high-resolution technique for fluid dynamics, Journal of Computational Physics, 228 (2009) · Zbl 1172.76034
[13] Berloff, P. S.; Karabasov, S. A.; Farrar, T.; Kamenkovich, I., On latency of multiple zonal jets in the oceans, Journal of Fluid Mechanics, 686, 534-567 (10 November 2011)
[14] Faranosov, G. A.; Goloviznin, V. M.; Karabasov, S. A.; Kondakov, V. G.; Kopiev, V. F.; Zaitsev, M. A., CABARET method on unstructured hexahedral grids for jet noise computation, (18th AIAA/CEAS Aeroacoustics Conference, 33rd AIAA Aeroacoustics Conference. 18th AIAA/CEAS Aeroacoustics Conference, 33rd AIAA Aeroacoustics Conference, Colorado Springs, Colorado (4-6 June 2012))
[15] Semiletov, V. A.; Karabasov, S. A.; Faranosov, G. A.; Zaitsev, M. A., Airfoil flow and noise computation using monotonically integrated LES and acoustic analogy, (18th AIAA/CEAS Aeroacoustics Conference, 33rd AIAA Aeroacoustics Conference. 18th AIAA/CEAS Aeroacoustics Conference, 33rd AIAA Aeroacoustics Conference, Colorado Springs, Colorado (4-6 June 2012))
[16] Unfer, T.; Boeuf, J.-P.; Rogier, F.; Thivet, F., An asynchronous scheme with local time stepping for multi-scale transport problems: application to gas discharge, Journal of Computational Physics, 227, 898-918 (2007) · Zbl 1128.65069
[17] Hirsch, C., Numerical Computation of Internal and External Flows, V2: Computational Method for Inviscid and Viscous Flows (1990), John Wiley & Sons Ltd.
[18] Thompson, K. W., Time dependant boundary conditions for hyperbolic systems. II, Journal of Computational Physics, 89, 439-461 (1990) · Zbl 0701.76070
[19] Kurbatskii, Konstantin A., Analytical solutions of the category 1, benchmark problems 1 and 2, (Tam, C. K.W.; Hardin, J. C., Second Computational Aeroacoustics (CAA) Workshop on Benchmark Problems (June 1997), National Aeronautics and Space Administration, Langley Research Center: National Aeronautics and Space Administration, Langley Research Center Hampton, Virginia)
[20] Sagrado, A. G.; Hynes, T. P., Wall pressure sources near an airfoil trailing edge under turbulent boundary layers, Journal of Fluids and Structures, 30, 3-34 (2012)
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.