Unified positional PFEM formulation for fluid-structure interaction prob- lems with free surface flows

Resumo

This paper aims to present a positional unified PFEM formulation to solve problems of free surface
flows interacting with elastic structures. In contrast with traditional FEM formulations of fluid mechanics that
use velocities, here we use nodal position as the main variables for both solid and fluid. In addition, the same
solution scheme is used to solve the governing equations of both physical problems. In fact, the coupled problem

is treated as an unique spatial domain containing two different materials. For the solid, a hyperelastic Saint-Venant-
Kirchhoff model is adopted, which is suited for large displacement analysis within the small strain regime, while

the fluid is considered to have an incompressible-Newtonian behavior. A mixed position-pressure approximation
is adopted for the fluid domain to ensure incompressibility, together with a Pressure Stabilizing Petrov-Galerkin
(PSPG). The time marching procedure is performed by means of the second order alpha-generalized scheme. The
usage of a Lagrangian description naturally allows the simulation of deformable solids and free surface flows as
the movement of the mesh nodes coincides with the physical particles motion. However, free surface flows tend
to deteriorate the mesh quality as topological changes and several distortions of the fluid domain may occur. To
deal with that, the PFEM plays a key role by constantly regenerating the mesh and automatically detecting the
physical boundaries by combining an efficient Delaunay triangulation-alpha-shape procedure. The applicability of
the developed approach is demonstrated by the simulation of selected problems.