Direct numerical simulations, where both the large and small scales in the flow are fully resolved, provide an excellent instrument to validate multiphase flow processes and also further our understanding of it. Three multiphase systems are studied using a finite difference/front-tracking method developed for direct numerical simulations of time-dependent system¬¬s. The purpose of these studies is to demonstrate the benefit in developing accurate sub-grid models that can be coupled with the direct numerical simulations to reduce the computational time. The primary reason to use the models is that the systems under consideration are sufficiently large that resolving the smallest scales is impractical. The processes that are examined are: (1) droplet motion and impact (2) nucleate boiling and (3) convective mass transfer. For droplet impact on solid walls and thin liquid films, the splash characteristics are studied. The collision of a fluid drop with a wall is examined and a multiscale approach is developed to compute the flow in the film between the drop and the wall. By using a semi-analytical model for the flow in the film we capture the evolution of films thinner than the grid spacing reasonably well. In the nucleate boiling simulations, the growth of a single vapor from a nucleation site and its associated dynamics are studied. The challenge here is the accurate representation of the nucleation site and the small-scale motion near the wall. To capture the evaporation of the microlayer left behind as the base of the bubble expands we use a semi-analytical model that is solved concurrently with the rest of the simulations. The heat transfer from the heated wall, the evolution of the bubble size and the departure diameter are evaluated and compared with the existing numerical results. The mass transfer near the interface, without fully resolving the layer by refining the grid is accommodated by using a boundary layer approximation to capture it. The behavior of the concentration profile is taken to be self-similar. A collection of potential profiles is tested and the accuracy of each of these models is compared with the full simulations.