Explicit time stepping renders many high-resolution schemes in Computational Aeroacoustics to become less efficient when dealing with non-uniform meshes in multiple dimensions. In the present paper, the Compact Accurately Boundary-Adjusting high-REsolution Technique (CABARET) Euler scheme is extended to asynchronous time-stepping which allows it to significantly boost computational performance with non-uniform grids. Numerical examples for 1D and 2D CABARET with asynchronous time stepping are provided. For further demonstration of the CABARET's capabilities in 3D where the asynchronous time stepping is expected to bring a step change in the scheme efficiency, Large Eddy Simulation of subsonic flow over a NACA0012 airfoil at zero angle of attack is conducted. The aerodynamic and acoustic results obtained with a single time stepping CABARET method are compared with the experimental data available.
Get full access to this article
View all access options for this article.
References
1.
WolfW. and LeleS., Trailing Edge Noise Prediction Using Compressible LES and Acoustics Analogy, 17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference), Portland, Oregon, 5–8 June 2011
2.
DawsonC. and KirbyR., High resolution schemes for conservation laws with locally varying time steps, SIAM J. Sci. Comput. 22 (6), 2256, 2001
3.
OmelechenkoY.A.KarimabadiH.Self-adaptive time integration of flux-conservative equations with sources, Journal of Computational Physics216, 179–194, 2006
4.
OmelechenkoY.A.KarimabadiH., A time-accurate explicit multi-scale technique for gas dynamics, Journal of Computational Physics226, 282–300, 2007
5.
TamC.K.W. and KurbatskiiK.A., Multi-size-mesh multi-time-step dispersion-relatiion-preserving scheme for multiple-scales aeroacoustics problems, International Journal of Computational Fluid Dynamics, 17(2), 119–132, 2003
6.
ChangS.C.WuY.YangV. and WangX.Y., Local Time-Stepping Procedures for the Space-Time Conservation Element and Solution Element Method, International Journal of Computational Fluid Dynamics, Vol. 19, No 5, 359–380, July 2005
7.
UnferT.BoeufJ.-P.RogierF.ThivetF., An Asynchronous Scheme with Local Time Stepping for Multi-scale Transport Problems: Application to Gas Discharge, Journal of Computational Physics227, 898–918, 2007
8.
YenJ.C., Demonstration of a Multi-Dimansional Time-Accurate Local Time Stepping CESE Method, 17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference), Portland, Oregon, 5–8 June 2011
9.
GolovizninV.M., and SamarskiiA.A., Difference Approximation of Convective Transport with Spatial Splitting of Time Derivative, Mathematical Modelling, Vol. 10, No. 1, 86–100, 1998
10.
KarabasovS.A.GolovizninV.M., New Efficient High-Resolution Method for Nonlinear Problems in Aeroacoustics, AIAA Journal, Vol. 45, No 12, 2007
11.
GolovizninV.M.SemenovV.N.KorortkinI.A., and KarabasovS.A., “A novel computational method for modelling stochastic advection in heterogeneous media”. Transport in Porous Media, Springer Netherlands, 2007, 66(3), pp. 439–456.
12.
IserlesA., Generalized Leapfrog Methods, IMA Journal of Numerical Analysis, 6, 3, 1986
13.
RoeP.L., Linear bicharacteristic scheme without dissipation, SIAM J. Sci. Comput., 19, pp. 1405–1427, 1998
14.
KarabasovS.A.GolovizniV.M., Compact Accurately Boundary Adjusting high-REsolution Technique for Fluid Dynamics, J. Comput.Phys., 228, 2009
15.
TuckerP.G. and KarabasovS.A., “Unstructured grid solution of the eikonal equation for acoustics”, Int. J. Aeroacoustics, vol 8 (6), 2009, pp.535–554
16.
BerloffP.S.KarabasovS.A.FarrarT. and KamenkovichI., On Latency of Multiple Zonal Jets in the Oceans, Journal of Fluid Mechanics, 686, pp. 534–567, 10 November, 2011
17.
HirschC., Numerical Computation of Internal and External Flows,” V2: Computational Method for Inviscid and Viscous Flows, John Wiley & Sons Ltd, 1990
18.
ThompsonK.W., Time Dependant Boundary Conditions for Hyperbolic Systems,”II. Journal of Computational Physics, 89, pp. 439–461, 1990
19.
TamC.K.W. and HardinJ.C., Second Computational Aeroacoustics (CAA) Workshop on Benchmark Problems, National Aeronautics and Space Administration, Langley Research Center, Hampton, Virginia, June 1997
20.
SagradoA.G. and HynesT.P., Wall Pressure Near an Airfoil Trailing Edge Under Turbulent Boundary Layers, Fluid and Structures, 2011
21.
BrooksT.F.PopeD.S., and MarcoliniM.A., Airfoil Self-Noise and Prediction, NASA Reference Publication 1218, NASA, 1989
22.
FurebyC. and GrinsteinF.F., Large Eddy Simulation of High-Reynolds-Number Free and Wall-Bounded Flows, Journal of Computational Physics, Volume 181, Issue 1, 1 September 2002, Pages 68–97
WilliamsFfowcs E. and HawkingsD. L., Sound Generation by Turbulence and Surfaces in Arbitrary Motion, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 264, No. 1151, 8 May, 1969, pp. 321–342
