Restrictions on computing power make direct numerical simulation too expensive for complex flows; thus, the development of accurate large eddy simulation (LES) methods, which are industrially applicable and efficient, is required. This paper reviews recent findings about the leading order dissipation rate associated with high-resolution methods and improvements to the standard schemes for use in highly turbulent flows. Results from implicit LES are presented for a broad range of flows and numerical schemes, ranging from the second-order monotone upstream-centered schemes for conservation laws to very high-order (up to ninth-order) weighted essentially non-oscillatory schemes.