Effects of numerical dissipation on the interpretation of simulation results in computational fluid dynamics

The accuracy of direct and large-eddy simulations (DNS and LES) is typically assessed through a time consuming process of multiple runs and comparisons with available benchmark data. The goal is to achieve physically representative results by minimizing truncation errors in DNS, along with subgrid-scale modeling errors when performing LES. We show that even if these errors cannot be neglected, the physical accuracy can be improved if the numerical dissipation is properly accounted for in interpreting the results. Based on the balance of kinetic energy proposed by Schranner et al. [21], the method allows to compute the numerical dissipation rate and the numerical viscosity at each time step in a simulation for an arbitrary computational fluid dynamics (CFD) solver. We demonstrate that the quantitative knowledge of the numerical dissipation can be employed to better understand results obtained using dissipative CFD codes. We consider two different cases: DNS for a weakly turbulent wake past a sphere at Re=1000 performed using the OpenFOAM solver, and LES of a laminar separation bubble flow at Re=100,000 performed using a compact difference solver with stabilizing filters. The procedure is used to show that results of nominally under-resolved DNS (UDNS) can be re-interpreted as corresponding to LES results or to DNS results but for a different, effective Reynolds number that accounts for the total dissipation, consisting of the numerical dissipation and of the viscous dissipation. In both cases, comparison with benchmark data is much improved compared with cases when the nominal values used in the code are employed.