Hybrid algorithms for Direct Numerical Simulations of two-phase flows are designed to provide better solutions with respect to absolute accuracy, error convergence, numerical boundedness and volume (mass) conservation errors, compared to the combined original algorithms themselves. The algorithms developed so far support structured and Cartesian meshes as well as octree-based and block-structured local mesh refinement in the vicinity of the fluid interface.Using unstructured meshes for domain discretization represents a standard way to deal with flow domains of arbitrary geometrical complexity. Local dynamic Adaptive Mesh Refinement (AMR) enables efficient simulations of two-phase flows by providing accuracy where it is most needed: near the fluid interface.In this work we present a first to our knowledge hybrid Level Set/Front Tracking DNS method of two-phase that supports both accurate and very efficient computations on unstructured meshes. Additionally, calculations in both two-and-three dimensions are supported. The implementation has been developed within the OpenFOAM framework and is to be released as Open Source.