Abstract: The finite-volume TVD-LW N-S solvers were developed by using B-L model of high Re number k-ε model and low Re number k-ε model respectively.Some numerical examples have been calculated to demonstrate the resolving capability of the numerical method for boundary layer,separative region and shock.The advantage of B-L model is simplicity and convenience.The k-ε model has high adaptability,and can be divided to two types.One is low Re number k-ε model, for which the wall function is not used;and the other is high Re number k-ε model,for which the wall function is used.The precision of the low Re number k-ε model is better than that of high Re number k-ε model,but it requires more computer time,storage capacity,and larger grid.The k-ε model can predict boundary separation.For convectional calculation,high Re number k-ε model is more suitable as it can provide required precision with coarser grid.