Dispersion error comparison of non-dissipative schemes for scale-resolving simulations of turbulent flows

The question of how the velocity field is distorted in the simulations of turbulent flows by the large eddy simulation method in the presence of mean advection flow is studied. In this case, the resolved inhomogeneities of the solution move along the computational grid, inevitably subject to interpolation errors. Symmetric conservative finite-difference schemes with the property of conservation of kinetic energy and entropy of orders of accuracy 2, 4, and 6 are compared. In addition, versions of these schemes of orders of accuracy 2 and 4 with an optimized dispersion relation are considered. The results of simulations of the diagonal vortex convection problem are presented and a series of simulations of statistically stationary homogeneous turbulence, including in the presence of mean advection flow are analyzed. The degree of distortion of the longitudinal energy spectra is demonstrated. The question of the applicability of the basic second order of accuracy scheme is discussed.