Assessment measures for URANS/DES/LES: an overview with applications

A survey of quality assessment methods is presented covering a range of possible errors in applications of CFD. Beside modeling and numerical errors further uncertainties in unsteady flow simulations are related to inlet conditions and statistical averaging. The main focus is on measures that can be applied to unsteady Reynolds averaged Navier–Stokes (URANS) solvers, hybrid large eddy simulations (HLES), detached eddy simulations (DES), and mostly LES applications. The quantification of uncertainty in LES (large eddy simulations) is difficult for two reasons: (i) substantial grid refinement is too expensive and time consuming; (ii) the modeling errors and discretization errors are convoluted in such a nonlinear manner that it is difficult to segregate one from the other. In hybrid URANS/LES this task is even more difficult because the transitional regions cannot be identified a priori. A brief review of attempts to quantify the accuracy of LES focusing on Richardson extrapolation (RE) is presented. Selected measures are applied to URANS, DES and LES cases from the literature. An attempt is made to separate the modeling contribution from the numerical errors in LES. The methods proposed for the quantification of LES and DES accuracy are still in their infancy stage. Early results are however, promising.

Keywords:

• Assessment measures
• LES
• Unsteady RANS
• DES
• Modeling
• Numerical and statistical uncertainty
• Inlet boundary conditions

AMS Subject Classification: :

• 76F65
• 76F55
• 76F99

Acknowledgments

Contributions and help from the graduate students C. Ersahin, G. Hu, J. Li, S. Pakalapati, C. Shaffer and A. Burt and Dr. W. Huebsch of West Virginia University are greatly appreciated. Many thanks to Dr. D.K. Tafti and his student A. Wiswanathan for providing their DES data. Financial support by the DFG (German Research Council) SFB 568 is gratefully acknowledged.