Multi-fluid flows with the Particle Finite Element Method

Particle methods are those in which the problem is represented by a discrete number of particles. Each particle moves accordingly with its own mass and the external/internal forces applied on it. In this paper the Particle Finite Element Method based on finite element shape functions is used to solve the continuous fluid mechanics equations in the case of heterogeneous density. To evaluate the external applied forces to each particle, the incompressible Navier–Stokes equations are solved at each time step using a Lagrangian formulation. All the information in the fluid is transmitted via the particles. All kinds of density heterogeneous fluids and multiphase flows with internal interfaces including or not free-surfaces, breaking waves and fluid separations may be easily solved with this methodology.