Artificial and Eddy Viscosity in Large Eddy Simulation Part 2: Turbulence Models

Abstract

This is the second part to our companion paper. The novel method to quantify artificial dissipation proposed in Part 1 is further applied in turbulent channel flow at $\mathrm{Re_\tau}=180$ using various subgrid-scale models, with an emphasis on minimum-dissipation models (QR and AMD). We found that the amount of artificial viscosity is comparable to the eddy viscosity, but their distributions are essentially opposite. The artificial viscosity can either produce turbulent kinetic energy (TKE) in the near wall region or dissipate TKE in the bulk region. The eddy viscosity is almost uniformly distributed across the wall-normal direction and actively damps TKE at the channel center. An eddy viscosity level of $\nu_e/\nu < 22\%$ leads to accurate predictions of flow quantities at the current mesh resolution. The optimal coefficients for the QR model combined with symmetry-preserving discretization were found to be C=0.092 for turbulent kinetic energy and C=0.012 for Reynolds stress terms and large scale motions. Adjusting the QR model coefficient changes the artificial viscosity and significantly impact turbulence characteristics: small-scale motions remain unaffected, while larger scales are less accurately captured with larger coefficients. For error quantification, the SGS activity parameter $\nu_{rel} = \frac{\nu_e}{\nu_e + \nu}$ helps relate and reflect the error magnitude with the SGS model. Optimal coefficients for the AMD model were also identified. The trends of varying the coefficient are similar to the QR model but differ in the amplitude of changes. The AMD model is more sensitive to the model coefficients and introduces more eddy viscosity in the near-wall region compared to the QR model. This research highlights the importance of balancing numerical and eddy viscosities for accurate LES predictions.