The particle finite element method (PFEM): an effective numerical technique for solving marine, naval and harbour engineering problems

We present some developments in the Particle Finite Element Method (PFEM) for the solution of complex coupled problems in marine, naval and harbour engineering involving fluid-soil-structure interaction (FSSI). The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in a continuum domain containing fluid, soil/rock and structures subdomains. A mesh connects the nodes defining the discretized domain where the governing equations for each of the constituent materials are solved with the FEM. The stabilization for dealing with an incompressibility material is introduced via the finite calculus (FIC) method. An incremental iterative scheme for solving the non linear transient FSSI problem is described. The procedure to model frictional contact conditions and material erosion at fluid-solid and solid-solid interfaces is described. We present examples of application of the PFEM to solve FSSI problems in marine, naval and harbour engineering such as the motion of rocks by water streams, the stability of breakwaters and constructions under sea waves, the sinking of ships and the collision of a ship with ice blocks.