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A finite-difference Total Variation Diminishing (TVD) numerical simulation model for coupling the Reynolds Averaged Navier-Stokes (RANS) equations, pressure-relative continuity equation and various k-ε turbulence models was developed to solve the incompressible flow based on the pseudo-compressibility method. The hyperbolicity of all these equations was studied and the discretization of the fully coupling equations with all the primal variables and source terms were made in this article. Numerical simulation for modeling the flow around a ground-mounted square rib was implemented and validated by comparing with the published wind tunnel experimental data. It is shown that such a numerical simulation method with a proper turbulence model has a very good accuracy to simulate the flow around a surface-mounted rib. It is concluded that the Renormalization Group (RNG) and Chen-Kim k-ε turbulence models have much better ability to predict the characteristics of the vortex structure and flow separation than the standard k-ε model.