This work demonstrates a computational framework for simulating vaporizing, liquid-gas flows. It is developed for the general vaporization problem which solves the vaporization rate based as from the local thermodynamic equilibrium of the liquid-gas system. This includes the commonly studied vaporization regimes of film boiling and isothermal evaporation. The framework is built upon a Cartesian grid solver for low-Mach, turbulent flows which has been modified to handle multiphase flows with large density ratios. Interface transport is performed using an unsplit volume of fluid solver. A novel, divergence-free extrapolation technique is used to create a velocity field that is suitable for interface transport. Sharp treatments are used for the vapor mass fractions and temperature fields. The pressure Poisson equation is treated using the Ghost Fluid Method. Interface equilibrium at the interface is computed using the Clausius-Clapeyron relation, and is coupled to the flow solver using a monotone, unconditionally stable scheme. It will be shown that correct prediction of the interface properties is fundamental to accurate simulations of the vaporization process. The convergence and accuracy of the proposed numerical framework is verified against solutions in one, two, and three dimensions. The simulations recover first order convergence under temporal and spatial refinement for the general vaporization problem. The work is concluded with a demonstration of unsteady vaporization of a droplet at intermediate Reynolds number.