A detached-eddy simulation (DES) of a cylinder turbulent flow using a newly developed low diffusion E-CUSP (LDE) scheme with fifth-order WENO scheme is conducted. A conservative fourth-order accuracy finite central differencing scheme is used for the viscous terms. The computed results for the baseline grid agree well with the experiment. The solution sensitivity to spanwise length is investigated. The mesh refinement is performed. The results show that the mesh refinement has a significant effect on the DES simulation.