  Since the seminal work of Idelsohn, O\~nate and Del-Pin (2004), the Particle
Finite Element Method (PFEM) has relied on a Delaunay triangulation and the
Alpha--Shape (AS) algorithm in the remeshing process. This approach guarantees
a good quality of the Lagrangian mesh, but introduces a list of shortcomings
that demand geometrical treatments tailored to each problem. In order to
improve the remeshing process in PFEM, this work proposes the use of a
Level--Set (LS) function instead of the Alpha--Shape algorithm. Since the
Level--Set considers the boundary of the fluid and its interior, and not only a
geometric criterion as does the Alpha--Shape, the proposed strategy (PFEM--LS)
shows more robustness than the classical approach (PFEM--AS) owing to three
main improvements. First, the LS function allows for a better control over the
elements that are created during the fluid/fluid contact, which helps to reduce
mass creation. Second, it helps to preserve the smoothness of the free surface
and to reduce mass loss. Third, it allows the meshing of solitary particles
that are detached from the free surface, which improves the representation of
drops in PFEM. The methodology is presented and validated using free surface
flow problems in 2D.
