In this study, parametric studies on the artificial compressibility coefficient are performed to investigate convergence characteristics of the dual time stepping method. Convergence characteristics is evaluated by the residual of the continuity equation for various values of the artificial compressibility coefficient. For numerical simulations, Roe"s approximate Riemann solver in conjunction with a cell centered finite volume method is used. Numerical simulations are performed for unsteady problems with stationary and moving grids. The speed of convergence are compared in terms of the artificial compressibility coefficient. From the results, a proper range of the artificial compressibility coefficient to obtain a high speed of convergence are confirmed.