Abstarct: Free surface flows are of most interest in many engineering or mathematical problems and many methods have been developed for their numerical resolution in various fields of the physics or the engineering. In this thesis the volume of fluid method (VOF) is used for the numerical simulation of free surface flows involving an incompressible liquid and a compressible gas in order to model the flow in a Reservoir with a moving bottom surface with varying with time. The incompressible Navier-Stokes equations are assumed to hold in the liquid domain and have been solved numerically in developed two-dimensional grids, while the dynamical effects in the ideal gas are disregarded. Also all of the vortexes generated in the flow have been modeled and analyzed numerically. in laminar state the resulted circulation is closer to the right wall and the flow in the bottom right corner is sharper and the resulted circulation in the laminar flow is more symmetric.by solving the laminar flow in unsteady state and with Time step=0.1 , after passing a time of about 30.1 seconds the flow reaches to the steady state and no changes are observed in the circulation.in the turbulant state, the liquid reaches to the steady states after 127.7seconds. shear stress magnitude in term of position in turbulent and laminar state are compared with together. As it expected, the laminar flow reaches to the steady state sooner while the turbulent flow,at the same time is in the middle part. Comparisons of the computed results with exact solutions showed that the method is capable of achieving high accuracy and efficiency with minimal computational effort.