Analysis of errors occurring in large eddy simulation

We analyse the effect of second- and fourth-order accurate central finite-volume discretizations on the outcome of large eddy simulations of homogeneous, isotropic, decaying turbulence at an initial Taylor Reynolds number $Re_\lambda=100.$ We determine the implicit filter that is induced by the spatial discretization and show that a higher order discretization also induces a higher order filter, i.e. a low-pass filter that keeps a wider range of flow scales virtually unchanged. The effectiveness of the implicit filtering is correlated with the optimal refinement strategy as observed in an error-landscape analysis based on Smagorinsky's subfilter model. As a point of reference, a finite-volume method that is second-order accurate for both the convective and the viscous fluxes in the Navier-Stokes equations is used. We observe that changing to a fourth-order accurate convective discretization leads to a higher value of the Smagorinsky coefficient $C_S$ required to achieve minimal total error at given resolution. Conversely, changing only the viscous flux discretization to fourth-order accuracy implies that optimal simulation results are obtained at lower values of $C_S.$ Finally, a fully fourth-order discretization yields an optimal $C_S$ that is slightly lower than the reference fully second-order method.