Modeling and discretization errors in large eddy simulations of hydrodynamic and magnetohydrodynamic channel flows

We assess the performances of three different subgrid scale models in large eddy simulations (LES) of turbulent channel flows. Two regimes are considered: hydrodynamic and magnetohydrodynamic (i.e. in the presence of a uniform wall-normal magnetic field). The simulations are performed using a second-order finite volume (FV) and a pseudo-spectral (PS) method. The LES results are compared with under-resolved results (obtained without model) and direct numerical simulations (DNS). We show that discretization errors affect the FV results in two ways: (1) the flow statistics differ from the spectral estimates in the absence of subgrid model; and (2) the eddy viscosity systematically underestimates the spectral value in the presence of a subgrid model. This is mainly because numerical errors affect the computation of the derivatives, and in particular, they lower the discrete strain rate appearing in the viscous term and the subgrid model. The magnitude of the numerical errors further varies with the mesh resolution and the intensity of the turbulent fluctuations. In this manuscript, a novel formulation of the discrete strain, which was proven successful in homogeneous isotropic turbulence, is used to compute the FV eddy viscosities. Although the average norm of the discrete strain is largely increased using this formulation, the effect on the flow dynamics is marginal. This is explained by analysing the contribution of each term of the discrete kinetic energy balance. It is shown how the underestimation of the discrete viscous dissipation inhibits the effect of the improved discrete strain.