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The dissipative and dispersive properties of Hermite methods are analyzed by a modified equation approach and by direct computation of the dispersion relations for the discrete modes of the scheme. The two approaches lead to the same results for well-resolved modes but are quantitatively different at the finest scales. The resolution requirements, obtained from the analysis, for Hermite schemes are compared to those of typical high-resolution difference formulas. The results from the analysis are also used to predict the resolution requirements for a simulation at Re  3600. The validity of the prediction is confirmed by numerical experiments.

An Analysis of Dispersion and Dissipation Properties of Hermite Methods and its Application to Direct Numerical Simulation of Jet Noise