This paper is to compare the performance of recently developed low diffusion E-CUSP (LDE) scheme and Roe scheme when they are coupled with Spalart-Allmaras one equation turbulence model. The purpose is not just to understand their performance for RANS calculation. Such understanding is very useful for Detached Eddy Simulation(DES), for which the Spalart DES model is numerically based on Spalart-Allmaras one equation turbulence model. The algebraic Baldwin-Lomax turbulence model is also used as a reference to compare their numerical performance. The implicit Gauss-Seidel Line relaxation is used for time marching. For the Roe scheme, the implicit Jacobian matrix is based on the Roe scheme itself. For the LDE scheme, the implicit Jacobian is based on the Van Leer's flux vector splitting scheme. The finding of this research is: for the Baldwind-Lomax model, which does not introduce extra transport equation, both the LDE and the Roe scheme can use high CFL numbers and achieve high convergence rates; for the Spalart-Allmaras one equation turbulence model, the extra equation changes the Jacobian of the Roe scheme and weakens the diagonal dominance. It reduces the maximum CFL number permitted by the Roe scheme and hence decreases the convergence rate. The LDE scheme is only slightly affected by the extra equation and maintain high CFL number and convergence rate. Several 2D and 3D problems are calculated.