Abstract

The objective of this work is the derivation and implementation of a unified Finite
Element formulation for the solution of fluid and solid mechanics, Fluid-Structure Inter- action
(FSI) and coupled thermal problems.

The unified procedure is based on a stabilized velocity-pressure Lagrangian formulation. Each time
step increment is solved using a two-step Gauss-Seidel scheme: first the linear momentum equations
are solved for the velocity increments, next the continuity equation
is solved for the pressure in the updated configuration.

The Particle Finite Element Method (PFEM) is used for the fluid domains, while the
Finite Element Method (FEM) is employed for the solid ones. As a consequence, the domain is
remeshed only in the parts occupied by the fluid.

Linear shape functions are used for both the velocity and the pressure fields. In order to deal
with the incompressibility of the materials, the formulation has been stabilized using an updated
version of the Finite Calculus (FIC) method. The procedure has been derived for
quasi-incompressible Newtonian fluids. In this work, the FIC stabilization procedure has been
extended also to the analysis of quasi-incompressible hypoelastic
solids.
Specific attention has been given to the study of free surface flow problems. In particular,
the mass preservation feature of the PFEM-FIC stabilized procedure has been deeply studied with the
help of several numerical examples. Furthermore, the conditioning of the problem has been analyzed
in detail describing the effect of the bulk modulus on the numerical scheme. A strategy based on
the use of a pseudo bulk modulus for improving the conditioning of the linear system is also
presented.

The unified formulation has been validated by comparing its numerical results to ex- perimental
tests and other numerical solutions for fluid and solid mechanics, and FSI problems. The
convergence of the scheme has been also analyzed for most of the prob-
lems presented.
The unified formulation has been coupled with the heat tranfer problem using a staggered
scheme. A simple algorithm for simulating phase change problems is also described. The numerical
solution of several FSI problems involving the temperature is given.

The thermal coupled scheme has been used successfully for the solution of an industrial problem.
The objective of study was to analyze the damage of a nuclear power plant pressure vessel induced
by a high viscous fluid at high temperature, the corium.  The
numerical study of this industrial problem has been included in this work.

Abstract

This paper presents a purely Lagrangian approach for the 3D simulation of Bingham free-surface uids and their interaction with deformable solid structures.

In the proposed numerical strategy, the fluid is handled using the Particle Finite Element Method (PFEM) to tackle the issues resulting from extreme changes of geometry, such as mesh distortion and free-surface evolution. Additionally, the Papanastasiou model is employed as a regularization technique to overcome the

computational difficulties associated with the classical Bingham model. The solid structure, on the other hand, is represented by the hypoelastic constitutive model and simulated using the conventional Finite Element Method (FEM). The coupling between the fluid and the structure is achieved via a monolithic approach, called Unified formulation. Several numerical examples are presented to illustrate the correctness and the robustness of the proposed formulation, in 2D and in 3D. Special attention is devoted to the analysis of the convergence behavior of the proposed computational framework, the effect of the regularization on the numerical results and the 3D effects. Moreover, detailed comparisons between the simulated results and experimental data are performed so that the concerned problems and results can serve as benchmarks.