Highly deforming domains are a recurring problem in fluid mechanics. In domains bounded by a free surface, for instance, the evolving boundaries need to be tracked or captured. The Particle Finite Element Method, or PFEM, tackles this problem by considering the mesh to be an inherent part of the solution. Indeed, this Lagrangian-based strategy solves the Navier-Stokes equations on a finite element mesh, which is constantly deformed in such a way that it exactly represents the fluid domain. In this work, we propose an approach to adapt the mesh with a robust algorithm and theoretical guarantees on quality. The approach is based on Delaunay refinement strategies, and addresses well-known problems in PFEM of volume variation errors due to undesired element removal and addition. Our approach to PFEM is first presented. Next, the mesh adaptation algorithm is described, followed by simulation results.