be avoided if aliasing errors are small compared to truncation errors.
Aliased and dealiased numerical simulations of a turbulent channel flow are performed using spectral and finite difference methods.
The problem of aliasing errors in spectral simulations
Analytical and numerical studies show that aliasing errors are more of turbulent flows has been discussed in the literature [4][5][6][7]. destructive for spectral and high-order finite-difference calculations It has been demonstrated that, depending on the form of than for low-order finite-difference simulations. Numerical errors the nonlinear terms [5] in the Navier-Stokes equations, have different effects for different forms of the nonlinear terms in aliased spectral simulations can become unstable, exhibit the Navier-Stokes equations. For divergence and convective forms, spectral methods are energy-conserving only if dealiasing is per-decay, or give reasonable results. Zang [5] performed sevformed. For skew-symmetric and rotational forms, both spectral eral spectral simulations of transition and turbulence in and finite-difference methods are energy-conserving even in the incompressible flow and reported that, without dealiasing, presence of aliasing errors. It is shown that discrepancies between the simulations with convective and divergence forms of the results of dealiased spectral and standard nondialiased finitethe nonlinear terms were numerically unstable, whereas difference methods are due to both aliasing and truncation errors with the latter being the leading source of differences. The relative the computations with the rotational form produced inacimportance of aliasing and truncation errors as compared to subgrid curate results. The aliasing errors associated with the rotascale model terms in large eddy simulations is analyzed and distional form were reported to be even more damaging in cussed. For low-order finite-difference simulations, truncation ersimulations of transition. The poor behavior of the rotarors can exceed the magnitude of the subgrid scale term. แฎ 1997 tional form was also reported earlier by Horiuti [8] who Academic Press carried out large eddy simulations of turbulent channel flow. No dealiasing was performed in that study. Horiuti found that turbulence decayed when the rotational form 310