This paper presents a novel approach to simulating surface tension flow within a position-based dynamics (PBD) framework. We enhance the conventional PBD fluid method in terms of its surface representation and constraint enforcement to furnish support for the simulation of interfacial phenomena driven by strong surface tension and contact dynamics. The key component of our framework is an on-the-fly local meshing algorithm to build the local geometry around each surface particle. Based on this local mesh structure, we devise novel surface constraints that can be integrated seamlessly into a PBD framework to model strong surface tension effects. We demonstrate the efficacy of our approach by simulating a multitude of surface tension flow examples exhibiting intricate interfacial dynamics of films and drops, which were all infeasible for a traditional PBD method.