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

We present some developments in the Particle Finite Element Method (PFEM) for analysis of coupled problems in mechanics involving fluid-soil-structure interaction (FSSI). The PFEM uses an updated Lagrangian description to model the motion of material points in both the fluid and the solid domains (the later including soil/rocks and structures). A mesh connects the particles (nodes) defining the discretized domain where the governing equations for each of the constituent materials are solved as in the standard FEM. The procedure to model frictional contact conditions and material erosion at fluid-solid and solid-solid interfaces is described. We present several examples of application of the PFEM to solve FSSI problems such as the motion of rocks by water streams, the erosion of river beds, the stability of breakwaters and constructions under sea waves, the falling of landslides on houses and into a reservoir and the failure of rockfill dams in overspill situations.

Abstract

El deflectòmetre d’impacte segurament és l’aparell més utilitzat per realitzar assaigs no destructius dels ferms. Els enginyers utilitzen el deflectòmetre d’impacte per estimar els mòduls elàstics de les diferents capes que conformen el ferm assumint una aproximació quasi estàtica del fenomen. Amb la utilització del Mètode dels Elements Finits i les Partícules (PFEM), per una banda es pot simular l’impacte que provoca el deflectòmetre d’impacte sobre el ferm, i de l’altra validar el PFEM com a model axisimètric de resposta dinàmica d’un ferm.

La validació consisteix a comparar la concavitat de deflexions mesurada pel deflectòmetre d’impacte amb la concavitat de deflexions calculada amb el PFEM utilitzant els mòduls elàstics que proporciona el càlcul invers.

Els capítols 2 i 3 inclouen el marc teòric en el qual es desenvolupa el treball. El capítol 2 inclou una introducció als ferms, presenta el concepte de deflexió, fa un repàs dels equips d’avaluació no destructiva i presenta un resum dels diferents mètodes existents per al càlcul de paviments flexibles. El capítol 3 és una introducció al Mètode dels Elements Finits i les Partícules.

El capítol 4 presenta els desenvolupaments dels objectius plantejats.

Per últim, es presenten unes consideracions finals, que inclouen les conclusions, possibles millores del programa d’ordinador emprat i propostes de futures línies d’investigació.

Els annexes inclouen els resultats de tots els casos calculats amb les taules i les gràfiques corresponents.

Abstract

We present some developments in the formulation of the Particle Finite Element Method (PFEM) for analysis of complex coupled problems in fluid and solid mechanics accounting for fluid-structure interaction and coupled thermal effects. The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are viewed as material points which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility of the fluid is introduced via the finite calculus (FIC) method. An incremental iterative scheme for the solution of the non linear transient coupled fluid-structure problem is described. Extensions of the PFEM to allow for frictional contact conditions at fluid-solid and solid-solid interfaces via mesh generation are described. A simple algorithm to treat erosion in the fluid bed is presented. Examples of application of the PFEM to solve a number of coupled problems such as the effect of large wave on structures, the large motions of floating and submerged bodies, bed erosion situations and melting and dripping of polymers under the effect of fire are given.

Abstract

In this work we extend the Particle Finite Element Method (PFEM) to multi-fluid flow problems with the aim of exploiting the fact that Lagrangian methods are specially well suited for tracking interfaces. We develop a numerical scheme able to deal with large jumps in the physical properties, included surface tension, and able to accurately represent all types of discontinuities in the flow variables. The scheme is based on decoupling the velocity and pressure variables through a pressure segregation method which takes into account the interface conditions. The interface is defined to be aligned with the moving mesh, so that it remains sharp along time, and pressure degrees of freedom are duplicated at the interface nodes to represent the discontinuity of this variable due to surface tension and variable viscosity. Furthermore, the mesh is refined in the vicinity of the interface to improve the accuracy and the efficiency of the computations. We apply the resulting scheme to the benchmark problem of a two-dimensional bubble rising in a liquid column presented in [[#cite-1|[1]]], and propose two breakup and coalescence problems to assess the ability of a multi-fluid code to model topology changes.

Abstract

Landslides in reservoirs constitute one of the main threats to dams. Although they are not frequent, they may generate severe damages in the population and goods placed near the shores. It is a complex phenomenon, because of the interaction between the landslide, the still water in the reservoir, and the dam. The Particle Finite Element Method (PFEM) is an innovative numerical scheme which combines a lagrangian approach with the resolution of FEM equations via mesh generation. In previous works, it had been applied to the simulation of landslides in reservoirs, considering the moving body either as a rigid solid or as a Newtonian fluid. Despite the promising results of the simulation of some reference cases, these constitutive models showed poor performance when applied to other relevant events, such as Vaiont case. Current work introduces the implementation of a non Newtonian Bingham model in the particle finite element method scheme, and the results of its application to several benchmark cases. Some of them have been used to calibrate the parameters of the Bingham model, whereas others served as test cases. The phenomenon presents several intrinsic uncertainties, such as the lack of precise information about the physical properties of the landslide, its geometry, its granulometry, the drag coefficient along the sliding surface, among others. In spite of that, results show that the Bingham model implemented can be useful for estimating the potential consequences of landslides in reservoirs. This implementation makes the PFEM a versatile numerical tool for the analysis of landslides in reservoirs, provided that from now on both rigid solids, Newtonian and non Newtonian fluids can be accounted for. The authors are currently working in the optimization of the numerical code, so that more complex problems could be afforded in more detail. In addition, the erosion module is being validated, in order to reproduce effects such as the dragging of the underlying material due to the landslide, as well as the effect of overtopping on dam stability, particularly for rockfill dams.

Abstract

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. '''Key words: '''Fluid-Structure interaction, Particle methods, Lagrange formulations, Incompressible Fluid Flows, Meshless Methods, Finite Element Method.

Abstract

In this work, a second-order semi-Lagrangian particle finite element method (SL-PFEM) is presented. The method is based on the second order velocity Verlet algorithm, using an explicit scheme to integrate the particles’ trajectories, and an implicit Crank-Nicholson scheme to integrate the particle’s velocities. The projection of the particle´s intrinsic variables onto the finite element (FE) mesh is based on a second-order global least-square. The elliptic part of the Navier-Stokes equations is discretized with the Crank-Nicholson scheme and solved using an iterative process. The method is verified against available analytical solutions, and applied to the classic flow around a cylinder problem.

Abstract

In this work we extend the Particle Finite Element Method (PFEM) to multi-fluid flow problems with the aim of exploiting the fact that Lagrangian methods are specially well suited for tracking interfaces. We develop a numerical scheme able to deal with large jumps in the physical properties, included surface tension, and able to accurately represent all types of discontinuities in the flow variables. The scheme is based on decoupling the velocity and pressure variables through a pressure segregation method which takes into account the interface conditions. The interface is defined to be aligned with the moving mesh, so that it remains sharp along time, and pressure degrees of freedom are duplicated at the interface nodes to represent the discontinuity of this variable due to surface tension and variable viscosity. Furthermore, the mesh is refined in the vicinity of the interface to improve the accuracy and the efficiency of the computations. We apply the resulting scheme to the benchmark problem of a two-dimensional bubble rising in a liquid column presented in [1], and propose two breakup and coalescence problems to assess the ability of a multi-fluid code to model topology changes.

Abstract

This work proposes a fully Lagrangian formulation for the numerical modeling of free-surface particle-laden flows. The fluid phase is solved using the particle finite element method (PFEM), while the solid particles embedded in the fluid are modeled with the discrete element method (DEM). The coupling between the implicit PFEM and the explicit DEM is performed through a sub-stepping staggered scheme. This work only considers suspended spherical particles that are assumed not to affect the fluid motion. Several tests are presented to validate the formulation. The PFEM–DEM results show very good agreement with analytical solutions, laboratory tests and numerical results from alternative numerical methods.