decade as they provide less numerical dissipation and do not require a kinetic energy conservation property to con-This paper proposes some new wavenumber-extended high-order upwind-biased schemes. The dispersion and dissipation errors trol the aliasing error . In general, although the highof upwind-biased finite-difference schemes are assessed and comorder upwind schemes cannot offer the same resolution pared by means of a Fourier analysis of the difference schemes. characteristics as spectral methods, they are computation-Up to 11th-order upwind-biased schemes are analyzed. It is shown ally more efficient and robust and can be easily implethat both the upwind-biased scheme of order 2N ฯช 1 and the corremented in complex geometries. Following Lele [7], resolusponding centered differencing scheme of order 2N have the same dispersion characteristics; thus the former can be considered to be tion (characteristics) in this paper means the accuracy of the latter plus a correction that reduces the numerical dissipation. numerical representation of the solution over the full range
The new second-order wavenumber-extended scheme is tested and of length scales that are resolvable on a mesh. Numerical compared with some well-known schemes. The range of wavenumspatial resolution has also been improved remarkably in bers that are accurately treated by the upwind-biased schemes is improved by using additional constraints from the Fourier analysis the past decade as a result of the development of larger to construct the new schemes. The anisotropic behavior of the disand faster computers, and has resulted in additional popupersion and dissipation errors is also analyzed for both the convenlarity of high-order schemes. Rai and Moin [6] revisited a tional and the new wavenumber-extended upwind-biased finitefinite-difference method for a direct simulation of fully difference schemes. แฎ 1997 Academic Press developed turbulent channel flow and presented a fifthorder upwind-biased scheme [8]. This fifth-order scheme was evaluated by Tamamidis and Assanis [9] against the 235