Discretization errors in large eddy simulation: on the suitability of centered and upwind-biased compact difference schemes

The suitability of high-order accurate, centered and upwind-biased compact difference schemes for large eddy simulation (LES) is evaluated through the static and dynamic analyses. For the static error analysis, the power spectra of the finite-differencing and aliasing errors are evaluated in the discrete Fourier space, and for the dynamic error analysis LES of isotropic turbulence is performed with various dissipative and non-dissipative schemes. Results from the static analysis give a misleading conclusion that both the aliasing and finite-differencing errors increase as the numerical dissipation increases. The dynamic analysis, however, shows that the aliasing error decreases as the dissipation increases and the finite-differencing error overweighs the aliasing error. It is also shown that there exists an optimal upwind scheme of minimizing the total discretization error because the dissipative schemes decrease the aliasing error but increase the finite-differencing error. In addition, a classical issue on the treatment of nonlinear term in the Navier–Stokes equation is revisited to show that the skew-symmetric form minimizes both the finite-differencing and aliasing errors. The findings from the dynamic analysis are confirmed by the physical space simulations of turbulent channel flow at Re=23000 and flow over a circular cylinder at Re=3900.