Fluid–structure interaction using the particle finite element method

In the present work a new approach to solve fluid–structure interaction problems is described. Both, the equations of motion for fluids and for solids have been approximated using a material (Lagrangian) formulation. To approximate the partial differential equations representing the fluid motion, the shape functions introduced by the meshless finite element method (MFEM) have been used. Thus, the continuum is discretized into particles that move under body forces (gravity) and surface forces (due to the interaction with neighboring particles). All the physical properties such as density, viscosity, conductivity, etc., as well as the variables that define the temporal state such as velocity and position and also other variables like temperature are assigned to the particles and are transported with the particle motion. The so called particle finite element method (PFEM) provides a very advantageous and efficient way for solving contact and free-surface problems, highly simplifying the treatment of fluid–structure interactions.