Abstract

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 [Oñate et al.]. The efficiency of the proposed strategy is tested by solving benchmark FSI problems.

Abstract

The purpose of this paper is to study the effect of the bulk modulus in the iterative matrix for the analysis of quasi-incompressible free surface fluid flows using a mixed Lagrangian finite element formulation and a partitioned solution scheme. A practical rule to set up the value of a pseudo-bulk modulus a priori in the tangent bulk stiffness matrix for improving the conditioning of the linear system of algebraic equations is also given. The efficiency of the proposed strategy is tested in several problems analyzing the advantage of the modified bulk tangent matrix with regard to the stability of the pressure field, the convergence rate and the computational speed of the analyses. The technique has been tested on the FIC/PFEM Lagrangian formulation presented in [19] but it can be easily extended to other quasi-incompressible stabilized finite element formulations. Copyright c 2010 John Wiley & Sons, Ltd.