A Framework to Assess the Quality and Robustness of Les Codes

We present a framework which can be used to rigorously assess and compare large-eddy simulation methods. We apply this to LES of homogeneous isotropic turbulence using a Smagorinsky model and three different discretizations. By systematically varying the simulation resolution and the Smagorinsky coefficient, one can determine parameter regions for which one, two or multiple flow predictions are simultaneously predicted with approximately minimal error. To this end errors on the predicted longitudinal integral length scale, the resolved kinetic energy and the resolved enstrophy are considered. Parameter regions where all considered errors are simultaneously (nearly) minimal are entitled ‘multi-objective optimal’ parameter regions. Surprisingly, we find that a standard second-order method has a larger ‘multi-objective optimal’ parameter region than two considered fourth order methods. Moreover, the errors in the re∗Also at: Dept. Mech. Engn., Katholieke Univ. Leuven, Celestijnenlaan 300A, B3001 Leuven, Belgium. Email: [email protected] †Also at: Anisotropic Turbulence, Fluid Dynam. Lab., Dept. Appl. Phys., Eindhoven Univ. Technol., P.O. Box 531, 5600 MB Eindhoven, The Netherlands spective ‘multi-objective optimal’ regions are also lowest for the second-order scheme. NOMENCLATURE Cs Smagorinsky coefficient. Ĉs Optimal refinement trajectory. C̃s Multi-objective optimal refinement trajectory. E Resolved turbulent kinetic energy. E Resolved enstrophy. L Longitudinal integral length scale. N Simulation resolution. δp Relative error. Ω Near optimal region.