Commun. Comput. Phys., 12 (2012), pp. 1603-1622.

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

Helen C. Yee 1*, Bjorn Sjogreen 2, Abdellah Hadjadj 3

1 NASA-Ames Research Center, Moffett Field, CA, 94035, USA.
2 Lawrence Livermore National Laboratory, Livermore, CA, 94551, USA.
3 CORIA UMR 6614 & INSA de Rouen, 76800 St-Etienne du Rouvray, France.

Received 26 November 2011; Accepted (in revised version) 13 April 2012
Available online 11 June 2012


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 & Sjogreen 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.

AMS subject classifications: 65Z05, 65M06, 65M50, 65M55, 65M60, 65M99, 65Y99

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Key words: High order numerical methods, numerical methods for turbulence with shocks, DNS, LES, mixing layer.

*Corresponding author.
Email: (H. C. Yee), (B. Sjogreen), (A. Hadjadj)

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