The ALE/Lagrangian Particle Finite Element Method: A new approach to computation of free-surface flows and fluid–object interactions

The Particle Finite Element Method (PFEM) is a well established numerical method [Aubry R, Idelsohn SR, Oñate E, Particle finite element method in fluid mechanics including thermal convection–diffusion, Comput Struct 2004;83:1459–75; Idelsohn S, Oñate E, Del Pin F, A Lagrangian meshless finite element method applied to fluid–structure interaction problems, Comput Struct 2003;81:655–71; Idelsohn SR, Oñate E, Del Pin F, The particle finite element method a powerful tool to solve incompressible flows with free-surfaces and breaking waves, Int J Num Methods Eng 2004;61:964–84] where critical parts of the continuum are discretized into particles. The nodes treated as particles transport their momentum and physical properties in a Lagrangian way while the rest of the nodes may move in an Arbitrary Lagrangian–Eulerian (ALE) frame. In order to solve the governing equations that represent the continuum, the particles are connected by means of a Delaunay Triangulation [Idelsohn SR, Oñate E, Calvo N, Del Pin F, The meshless finite element method, Int J Num Methods Eng 2003;58(4)]. The resulting partition is a mesh where the Finite Element Method is applied to solve the equations of motion. The application of a fully Lagrangian formulation on the particles provides a natural and simple way to track free surfaces as well as to compute contacts in an accurate and robust fashion. Furthermore, the usage of an ALE formulation allows large mesh deformation with larger time steps than the full Lagrangian scheme.