A set of governing equations to describe gas-liquid flows with phase change in the low Mach number limit will be presented. The system of equations accommodates local volume change at the gas-liquid interface due to condensation and evaporation while the total volume of the gas-liquid mixture remains constant. The framework is useful for simulating flows in computational domains that only use combinations of periodic and wall boundary conditions (e.g., isotropic turbulence and turbulent channel flow). Also, compared to the fully compressible formulation, this approach has the advantage of removing acoustic effects from the problem. Using the volume-of-fluid approach, a numerical method to solve the system of equations is developed. The cases of an evaporating and condensing droplet in a closed vessel are solved numerically, and the results show that the algorithm conserves mass while capturing the motion of the interface. The robustness of the method is demonstrated by performing DNS of an evaporating droplet in forced isotropic turbulence.