In the past, various authors have investigated the importance of aliasing errors in Fourier-based pseudo-spectral methods for direct numerical simulation (DNS) of turbulent flows (cf. \cite*{canuto:88} for a survey). The explicit removal of such errors has become common practice in numerical turbulence studies since the recognition of the 2/3-rule by \cite{orszag:71b} and the introduction of the relatively low-cost combination of phase-shifts and truncation by \cite{rogallo:81}. However, the importance of aliasing errors when using Chebyshev polynomial expansions instead of Fourier series has -- to my knowledge -- not been addressed in detail in the literature. While \cite{canuto:88} briefly describe the existence and possible removal of aliasing errors in Chebyshev pseudo-spectral methods, actual simulations of the Navier-Stokes equations have apparently been commonly performed without resorting to such corrections (e.g. \cite{kim:87}, \cite{krist:87}, \cite{hill:99}).

In the present report, we attempt to estimate whether the computational overhead due to the explicit removal of Chebyshev-induced aliasing errors is necessary (i.e. paying off in terms of efficiency) in a DNS of plane channel flow. We first recall the origin of aliasing errors in a Chebyshev method before turning to results from different test cases: analytical; transition to turbulence; fully-developed turbulence.

Our present results indicate that corrective action can slightly improve the quality of the solution in situations where the resolution is marginal. We do not find conclusive evidence that supports the use of the de-aliasing strategy under non-marginal conditions.