Influence of advection differencing error upon large-eddy simulation accuracy

Accurate prediction of turbulent features by a large-eddy simulation (LES) model requires accurate numerical evaluation of the nonlinear advective terms. In the presence of a mean wind, use of second-order or fourth-order finite differencing produces large losses of turbulent energy at high wavenumbers, an inaccuracy consistent with idealized numerical properties of these schemes. The discrete differencing inaccuracies also affect the small wavenumber "large eddy'' structure and the horizontally-averaged turbulent quantities. With a high accuracy pseudospectral technique, this energy loss does not occur and spectral behaviour corresponds to filtered Kolmogorov theory predictions out to the de-aliasing cutoff wavenumber. The inaccuracy of the finite difference schemes is greatly ameliorated through a Galilean transformation of the advective term.