# What is the PFEM?

#### Welcome Address

Welcome to the web page of the Particle Finite Element (PFEM). The PFEM is an innovative numerical method for solving a wide spectrum of problems involving the interaction of fluids and structures.

The main range of applications lay in the field of free-surface problems, fluid-structure interaction, problems where large deformation of the physical domain is observed and multiphase problems. The most typical applications include areas as Naval Engineering, Mold Filling, Casting problems, Multiphase Flows, Civil and Coastal Engineering, amongst others.

#### What is the PFEM?

The PFEM is a numerical method that uses a Finite Element mesh to discretize the physical domain and to integrate the differential governing equations. In contrast to classical Finite Element approximations, the nodes of the mesh move according to the equations of motion in a Lagrangian fashion. The nodes transport their momentum together with all their physical properties thus behaving as particles. At the end of each time step the mesh has to be rebuild as the nodes have been moved to their new time step position. For this reason a fast and robust algorithm to build the new mesh is essential. The Delaunay Tessellation is chosen to connect all the particles at the new time step position giving as a result a new mesh.

The resulting mesh not only works as a support where the differential equations are integrated, it is also used to identify the contacts and to track the free surface. This is accomplished with the help of a technique called alpha-shape. In a locally homogenous particle distribution the alpha-shape algorithm eliminates certain Delaunay circumcircles by means of a geometric criteria. The external faces of the remaining elements will define the boundaries.

#### Acknowledgements

The development of the PFEM at CIMNE is supported by a project of the National Programme of R+D in Spain coordinated by the Direccion General de Puertos in the Ministerio de Fomento.
The title of the project is "Development of a computer system based on a particle method for the analysis of wave-structures interaction in harbour structures".

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