A cell vertex finite volume algorithm and an artificial compressibility approach are employed to enable simulation of three-dimensional incompressible unsteady turbulent flow using unstructured tetrahedral meshes. Unsteady flow modeling is accomplished through the use of an implicit dual time stepping scheme, and stabilization of the procedure is achieved by the explicit addition of artificial viscosity in the Jameson–Schmidt–Turkel manner. The Spalart–Allmaras detached eddy simulation model is adopted for turbulent flow simulations. The computational performance is enhanced by the incorporation of multigrid acceleration and by parallelization of the solution algorithm. A number of examples are presented to demonstrate the capabilities of the resulting procedure.