The design of next generation internal combustion engines will require a more detailed understanding of the dynamics of fuel combustion. One way of studying this combustion process is through computational simulations of fuel injection, break-up and combustion processes. However, currently no computational fluid dynamic code is capable of simulating this entire process. The key missing aspect in simulating the fuel combustion process is resolving the vaporization process. As combustion occurs in the gas phase, a liquid fuel must vaporize before combustion can occur. The current dissertation demonstrates a computational framework for simulating such a vaporizing flow. The framework is built from the ground up starting from the laws of conservation of mass, momentum, and energy combined with the relevant thermodynamic relations. The framework discussed in this work will have a few properties that make it suitable towards the goal of simulating vaporizing multiphase flows. First, the solver is verified to produce convergent solutions, regardless of the thermodynamic regime of vaporization. Second, the actual implementation of vaporization sources is unconditionally stable, making simulation practical at all mesh resolutions. Both of these properties are important for performing simulations of real combustion configurations. This dissertation also includes a study on simulating droplet-laden turbulent flows, and explores the impact of flow turbulence on vaporization.