On the Effect of Numerical Errors in Large Eddy Simulations of Turbulent Flows

Aliased and dealiased numerical simulations of a turbulent channel flow are performed using spectral and finite difference methods. Analytical and numerical studies show that aliasing errors are more destructive for spectral and high-order finite-difference calculations than for low-order finite-difference simulations. Numerical errors have different effects for different forms of the nonlinear terms in the Navier–Stokes equations. For divergence and convective forms, spectral methods are energy-conserving only if dealiasing is performed. For skew-symmetric and rotational forms, both spectral and finite-difference methods are energy-conserving even in the presence of aliasing errors. It is shown that discrepancies between the results of dealiased spectral and standard nondialiased finite-difference methods are due to both aliasing and truncation errors with the latter being the leading source of differences. The relative importance of aliasing and truncation errors as compared to subgrid scale model terms in large eddy simulations is analyzed and discussed. For low-order finite-difference simulations, truncation errors can exceed the magnitude of the subgrid scale term.