Based on the velocity remapping strategy of the SALE algorithm, three methods are proposed to improve the accuracy and monotonicity of momentum flux calculation on a 1D staggered grid: the SUR method which employs the upwind-type slope and a repairing procedure; the SM method which employs a minmod slope limiter; and the SLR method which employs a new slope limiter and a repairing procedure. These methods are second-ordered, conservative and bound-preserving. They inherit advantages of simplicity and high efficiency of the SALE algorithm. They are easily generalized to the two-dimensional case.

A new subgrid eddy viscosity model is proposed. The new subgird eddy viscosity is proportional to the skewness of longitudinal velocity increment, which characterizes the transportation of turbulent momentum bteween resolved and unresolved turbulence. The new model is verified by a DNS data bank of isotropic turbulence, and has been applied to the turbulent channel flow. The results show to be in good agreement with DNS ones.