In the present study, a coupled level set and volume of fluid (CLSVOF) method is developed for two-dimensional unstructured grids to perform direct numerical simulations of two-phase flows including phase change. The volume fraction is advected using a multi-directional advection algorithm, where the flux polygons are constructed using vertex velocities and a scaling factor based on cell face velocities is used to correct the advected volume fraction. The level set field is advected using a total variational diminishing (TVD) scheme and geometrically reinitialized at the end of each time step. The performance of the proposed CLSVOF method is evaluated in detail on unstructured grids, both qualitatively and quantitatively, prior to simulation of phase change problems. A number of advection test cases and two-phase flow problems are considered for this purpose. Results obtained for film boiling over a horizontal flat plate using an unstructured grid show excellent agreement with results available in the literature. The numerical study of natural convection film boiling over a horizontal cylinder at different wall superheats shows a better agreement with semi-empirical correlations compared to other available numerical results. (C) 2018 Elsevier Ltd. All rights reserved.