Unified updated lagrangian formulation for the analysis of quasi and fully incompressible fluids and solids and their interaction via a partitioned scheme and the PFEM

In this work, a unified updated Lagrangian formulation for solving fluid-structure interaction (FSI) problems is derived. The mixed velocity-pressure formulation for hypoelastic solids and quasi and fully incompressible Newtonian fluids is obtained as an extension of the velocity formulation derived for a general continuum. The space discretization for the fluid domain is performed via the Particle Finite Element Method (PFEM), where for the solid domain a standard FEM is used. Linear interpolation is used for both the velocity and the pressure fields. The global FSI problem is solved using a Gauss-Seidel iterative scheme. The required stabilization for dealing with incompressible situations is given by an enhanced formulation of the Finite Calculus (FIC) technique [22]. The efficiency of the proposed strategy is tested by solving benchmark FSI problems.