Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T21:33:09.916Z Has data issue: false hasContentIssue false

Comparative Study of Three High Order Schemes for LES of Temporally Evolving Mixing Layers

Published online by Cambridge University Press:  20 August 2015

Helen C. Yee*
Affiliation:
NASA-Ames Research Center, Moffett Field, CA, 94035, USA
Bjorn Sjögreen*
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA, 94551, USA
Abdellah Hadjadj*
Affiliation:
CORIA UMR 6614 & INSA de Rouen, 76800 St-Etienne du Rouvray, France
*
Corresponding author.Email address:Helen.M.Yee@nasa.gov
Email address:sjogreen2@llnl.gov
Email address:hadjadj@coria.fr
Get access

Abstract

Three high order shock-capturing schemes are compared for large eddy simulations (LES) of temporally evolving mixing layers for different convective Mach numbers ranging from the quasi-incompressible regime to highly compressible supersonic regime. The considered high order schemes are fifth-order WENO (WENO5), seventh-order WENO (WENO7) and the associated eighth-order central spatial base scheme with the dissipative portion of WENO7 as a nonlinear post-processing filter step (WENO7fi). This high order nonlinear filter method of Yee & Sjögreen is designed for accurate and efficient simulations of shock-free compressible turbulence, turbulence with shocklets and turbulence with strong shocks with minimum tuning of scheme parameters. The LES results by WENO7fi using the same scheme parameter agree well with experimental results compiled by Barone et al., and published direct numerical simulations (DNS) work of Rogers & Moser and Pantano & Sarkar, whereas results by WENO5 and WENO7 compare poorly with experimental data and DNS computations.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Barone, M.F., Oberkampf, W.L. and Blottner, F.G., Validation Case Study: Prediction of Compressible Turbulent Mixing Layer Growth Rate, AIAA J., 44 (2006) 14881497.Google Scholar
[2]Bell, J. H. and Mehta, R. D., Development of a Two-Stream Mixing Layer from Tripped and Untripped Boundary Layers, AIAA J., 28 12 (1990) 2034-2042.CrossRefGoogle Scholar
[3]Bogdanoff, D. W., Compressibility Effects in Turbulent Shear Layers, AIAA J., 21 (1983) 926927.Google Scholar
[4]Chinzei, N., Masua, G., Komuro, T., Murakami, A., Kudou, K., Spreading of Two-Stream Supersonic Turbulent Mixing Layers, Phys. Fluids 29 (1986) 13451347.CrossRefGoogle Scholar
[5]Ducros, F., Laporte, F., Souleres, T., Guinot, V., Moinat, P., and Caruelle, B., High-order Fluxes for Conservative Skew-Symmetric-like Schemes in Structured Meshes: Application to Compressible Flows, J. Comput. Phys., 161 (2000) 114139.Google Scholar
[6]Ducros, F., Ferrand, V., Nicoud, F., Weber, C., Darracq, D., Gacherieu, C., and Poinsot, T., Large- Eddy Simulation of the Shock/ Turbulence Interaction, J. Comput. Phys., 152 (1999) 517549.CrossRefGoogle Scholar
[7]Farge, M., Pellegrino, G. and Schneider, K.Coherent Vortex Extraction in 3D Turbulent Flows using Orthogonal Wavelets, Phys. Rev. Lett., 5 (2001) 4501145014.Google Scholar
[8]Foysi, H., Sarkar, S., The Compressible Mixing Layer: an LES Study, Theor. Comp. Fluid Dyn., DOI: 10.1007/s00162-009-0176-8 (2010).CrossRefGoogle Scholar
[9]Gruber, M.R., Messersmith, N.L. and Dutton, J.C., Three-Dimensional Velocity Field in a Com-pressible Mixing Layer, AIAA Journal, 31 (1993) 20612067.Google Scholar
[10]Hadjadj, A. and Kudryavtsev, A., Computation and Flow Visualization in High Speed Aero-dynamics, J. Turbul., 6 (2005) 3381.Google Scholar
[11]Hadjadj, A., Yee, H.C. and Sjögreen, B., LES of temporally evolving mixing layers by an eighth-order filter scheme. International J. Num. Meth. Fluids, DOI: 10.1002/fld.2753 (2012).CrossRefGoogle Scholar
[12]Jiang, G.-S. and Shu, C.-W., Efficient Implementation of Weighted ENO Schemes, J. Comput. Phys., 126 (1996) 202228.Google Scholar
[13]Klein, M., Sadiki, A., and Janicka, J., A Digital Filter Based Generation of Inflow Data for Spatially Developing Direct Numerical or Large Eddy Simulation, J. Comp. Phys., 186 (2003) 652665.CrossRefGoogle Scholar
[14]Li, X.-S and Gu, C.-W., An All-Speed Roe-type Scheme and its Asymptotic Analysis of Low Mach Number Behaviour, J. Comput. Phys., 227 (2008) 51445159.Google Scholar
[15]Lo, S.-C., Blaisdell, G.A. and Lyrintzis, A.S., High-order Shock Capturing Schemes for Turbulence Calculations, Int. J. Numer. Meth. Fluids 62 (2010) 473498.Google Scholar
[16]Olsson, P. and Oliger, J., Energy and Maximum Norm Estimates for Nonlinear Conservation Laws, RIACS Technical Report, 94.01 (1994).Google Scholar
[17]Mahle, I., Sesterhenn, J. and Friedrich, R., Turbulent Mixing in Temporal Compressible Shear Layers Involving Detailed Diffusion Processes, J.Turb., 8 (2007) 12.Google Scholar
[18]Moin, P., Squires, K., Cabot, W. and Lee, S., A Dynamic Subgrid Scale Model for Compressible Turbulence and Scalar Transport, Phys. Fluids 3 (1991) 2746.CrossRefGoogle Scholar
[19]Pantano, C. and Sarkar, S., A Study of Compressible Effects in the High-Speed Turbulent Shear Layer Using Direct Simulation, J. Fluid Mech., 451 (2002) 329371.CrossRefGoogle Scholar
[20]Papamoschou, D., Roshko, A., The Compressible Turbulent Shear Layer: An Experimental Study, J. Fluid Mech., 197 (1988) 453477.Google Scholar
[21]Roe, P.L., Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes, J. Comput. Phys., 43 (1981) 357372.Google Scholar
[22]Rogers, M. M. and Moser, R. D., Direct Simulation of a Self-Similar Turbulent Mixing Layer, Phys. Fluids, 6 (1994) 903923.Google Scholar
[23]Samimy, M., Elliot, G.S., Effect of compressibility on the characteristics of free shear layer, AIAA J., 28(3) (1990) 439445.Google Scholar
[24]Samimy, M., Reeder, M.F., Elliott, G.S., Compressibility effects on large structures in free shear flows, Phys. Fluids, 4 (1992) 12511258.CrossRefGoogle Scholar
[25]Sjögreen, B. and Yee, H. C., Multiresolution Wavelet Based Adaptive Numerical Dissipation Control for Shock-Turbulence Computation, RIACS Technical Report TR01.01, NASA Ames Research Center (Oct 2000); also, J. Sci. Computing, 20 (2004) 211255.Google Scholar
[26]Sjögreen, B. and Yee, H.C., On Skew-Symmetric Splitting and Entropy Conservation Schemes for the Euler Equations, Proceedings of the 8th European Conference on Numerical Mathematics & Advanced Applications (ENUMATH 2009), Uppsala University, June 29 - July 2, 2009, Uppsala, Sweden.Google Scholar
[27]Sjögreen, B., Yee, H.C., Djomehri, M.J., Lazanoff, A., and Henshaw, W.D., Parallel Performance of ADPDIS3D - A High Order Multiblock Overlapping Grid Solver for Hypersonic Turbulence, Proceedings of the 21st International Conference on Parallel CFD, Moffett Field, CA, May 1822,2009.Google Scholar
[28]Sjögreen, B. and Yee, H.C., Variable High Order Multiblock Overlapping Grid Methods for Mixed Steady and Unsteady Multiscale Viscous Flows, Commun. Comput. Phys., 5 (2009), pp.730744.Google Scholar
[29]Stuart, A. and Humphries, A.R.Dynamical Systems and Numerical Analysis, Cambridge Monographs on Applied and Computational Mathematics, 1998.Google Scholar
[30]Wang, W., Yee, H.C., Sjögreen, B., Magin, T., and Shu, C.W., Construction of Low Dissipative High-Order Well-Balanced Filter Schemes for Nonequilibrium Flows, J. Comput. Phys., 230 (2011), pp 43164335. (doi:10.1016/j.jcp.2010.04.033,2010).Google Scholar
[31]Wang, W., Shu, C.W., Yee, H.C. and Sjögreen, B., High Order Finite Difference Methods with Subcell Resolution for Advection Equations with Stiff Source Terms, J. Comput. Physics, 231 (2012) 190214.Google Scholar
[32]Yee, H.C., Torczynski, J.R., Morton, S.A., Visbal, M.R., and Sweby, P.K., On Spurious Behavior of CFD Simulations, AIAA 971869, Proceedings of the 13th AIAA Computational Fluid Dynamics Conference, June 29 - July 2,1997, Snowmass, CO.; also Int. J. Num. Meth. Fluids, 30 (1999) 675711.Google Scholar
[33]Yee, H.C. and Sweby, P.K., Dynamics of Numerics & Spurious Behaviors in CFD Computations, Keynote paper, 7th ISCFD Conference, Sept. 1519,1997, Beijing, China, RIACS Technical Report 97.06, June 1997.Google Scholar
[34]Yee, H.C., Sandham, N.D., and Djomehri, M.J., Low Dissipative High Order Shock-Capturing Methods Using Characteristic-Based Filters, J. Comput. Phys., 150 (1999) 199238.Google Scholar
[35]Yee, H.C., Vinokur, M., and Djomehri, M.J., Entropy Splitting and Numerical Dissipation, J. Comput. Phys., 162 (2000) 3381.Google Scholar
[36]Yee, H.C. and Sjögreen, B., Designing Adaptive Low Dissipative High Order Schemes for Long-Time Integrations, In Turbulent Flow Computation, (Eds. Drikakis, D. & Geurts, B.), Kluwer Academic Publisher (2002); also RIACS Technical Report TR0128, Dec. 2001.Google Scholar
[37]Yee, H.C., Building Blocks for Reliable Complex Nonlinear Numerical Simulations, In Turbulent Flow Computation, (EdDrikakis, s. D. & Geurts, B.), Kluwer Academic Publisher (2002); also RIACS Technical Report TR0128, Dec. 2001.Google Scholar
[38]Yee, H.C. and Sjögreen, B., Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, II: Minimization of div(B) Numerical Error, J. Sci. Comp., 29 (2006) 115164.CrossRefGoogle Scholar
[39]Yee, H.C. and Sjögreen, B., Development of Low Dissipative High Order Filter Schemes for Multiscale Navier-Stokes/MHD Systems, J. Comput. Phys., 225 (2007) 910934.CrossRefGoogle Scholar
[40]Yee, H. C., Sjögreen, B., and Barone, M., High order numerical schemes for hypersonic flow simulations, VKI Lecture Series. Course on Hypersonic Entry and Cruise Vehicles, 30 June - 3 July 2008.Google Scholar
[41]Yee, H.C. and Sjögreen, B., High Order Filter Methods for Wide Range of Compressible Flow Speeds, Proceedings of ICOSAHOM 09 (International Conference on Spectral and High Order Methods). June 2226, 2009, Trondheim, Norway.Google Scholar
[42]Yee, H.C., Sjögreen, B., Local Flow Sensors in Controlling Numerical Dissipations for a Wide Spectrum of Flow Speed and Shock Strength, in preparation.Google Scholar
[43]Yee, H.C., Sjögreen, B., Shu, C.W., Wang, W., Magin, T. and Hadjadj, A., On Numerical Methods for Hypersonic Turbulent Flows, Proceedings of ESA 7th Aerothermodynamics Symposium, 912 May 2011 Site Oud Sint-Jan, Brugge, BelgiumASTRONUM-2010, June 1318,2010.Google Scholar
[44]Yee, H.C., Kotov, D. and Sjögreen, B., Numerical Dissipation and Wrong Propagation Speed of Discontinuities For Stiff Source Terms, Proceedings of the ASTRONUM-2011, June 1317, 2011, Valencia, Spain.Google Scholar