A two-dimensional Navier-Stokes flow solver is developed on unstructured triangular meshes. For turbulence closure. a standard high Reynolds number κ-ε model with a wall function boundary condition is used. The six equations of motion are discretized and integrated in a tightly coupled manner. The time integration is achieved using an explicit Runge-Kutta time-stepping scheme. The inviscid flux terms are discretized based on a cell-centered finite-volume formulation with Roe``s flux-difference splicing. The numerical method is applied for flows on a two-dimensional flat-plate. a backward-facing step, and a two-element airfoil. The results are compared with analytical and experimental data for validations.