Abstract

Unified formulation to solve fluid-structure interaction and multi-fluids problems are gaining popularity in many engineering applications, in particular for material forming processes. Indeed, it simplifies different issues related to mesh generation and boundary conditions and increases the flexibility to deal with multiscale problems.

We propose in this work a monolithic formulation where the complete problem is written in a fully Eulerian framework and the phases (fluid, solid,…) are separated by a level set function. The obtained system is solved using stabilized finite element methods. We combine this approximation with time-dependent anisotropic mesh adaptation to ensure accurate capturing of the discontinuities at the interfaces.

Different use of the levelset function ranging from, grain growth models for the evolutions of microstructure or void disclosure induced by forming operations, to the heat treatment of immersed metallic-alloys inside three-dimensional industrial furnaces will be presented. The advantages and the encountered numerical issues as well as the ongoing investigations related to these formulations will be discussed. 

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 a general formulation for analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use of a Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are thus viewed as particles 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, expressed in an integral from, are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility condition in the fluid is introduced via the finite calculus (FIC) method. A fractional step scheme for the transient coupled fluid-structure solution is described. Examples of application of the PFEM method to solve a number of fluid-structure interaction problems involving large motions of the free surface and splashing of waves are presented.

Abstract

The trading and investment decision processes in financial markets becomes ever more dependent on the use of valuation and risk models. In certain, cases such as risk management, modelling practice has become so homogeneous that one is led to ask about the effect this has on the price formation process. Furthermore, should stable price patterns emerge from this, can sophisticated investors who have private information about the use and characteristics of these models make superior gains? The aim of this article is to test this hypothesis in a stylised market environment, where a strategic trader who trades on information about the valuation and risk management models used by competitors. Results show that for our particular market setting, such a strategy has an advantage over those that do not use this information.

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

Designing large ultra-lightweight structures within a fluid flow, such as inflatable hangars in an atmospheric environment, requires an analysis of the naturally occurring fluid-structure interaction (FSI). To this end multidisciplinary simulation techniques may be used. The latter, though, have to be capable of dealing with complex shapes and large deformations as well as challenging phenomena like wrinkling or folding of the structure. To overcome such problems the method of embedded domains may be used. In this work we discuss a new solution procedure for FSI analyses based on the method of embedded domains. In doing so, we are in particular answering the questions: How to track the interface in the embedded approach, how does the subsequent solution procedure look like and how does both compare to the well-known Arbitrary Lagrangian-Eulerian (ALE) approach? In this context a level set technique as well as different mapping and mesh-updating strategies are developed and evaluated. Furthermore the solution procedure of a completely embedded FSI analysis is established and tested using different small- and large-scale examples. All results are finally compared to results from an ALE approach. It is shown that the embedded approach offers a powerful and robust alternative in terms of the FSI analysis of ultra-lightweight structures with complex shapes and large deformations. With regard to the solution accuracy, however, clear restrictions are elaborated.

Abstract

This presentation shows the recent work of the authors in the development of a time-domain FEM model for evaluation of the seal dynamics of a surface effect ship. The fluid solver developed for this purpose, uses a potential flow approach along with a stream-line integration of the free surface. The presentation focuses on the free surface-structure algorithm that has been developed to allow the simulation of the complex and highly dynamic behavior of the seals in the interface between the air cushion, and the water.

The developed fluid-structure interaction solver is based, on one side, on an implicit iteration algorithm, communicating pressure forces and displacements of the seals at memory level and, on the other side, on an innovative wetting and drying scheme able to predict the water action on the seals. The stability of the iterative scheme is improved by means of relaxation, and the convergence is accelerated using Aitken’s method.

Several validations against experimental results have been carried out to demonstrate the developed algorithm.

Abstract

The objective of this monograph is the derivation and implementation of a robust Finite Element formulation for the solution of solid-pore fluid coupled problems in multi-fractured porous media.

A coupled displacement-pore pressure FEM formulation for solving solid-pore fluid interaction problems is first introduced. The interaction between both components is governed by two equations: the balance of momentum for the mixture solid-fluid and the mass balance for the pore fluid.

Under nearly undrained-incompressible conditions, such formulation suffers from instability problems because of the violation of Babuska-Brezzi conditions. In order to work with elements of equal order interpolation for the displacement and pore pressure, the formulation is stabilized by means of the Finite Increment Calculus method (FIC). The FIC-stabilized formulation is tested against stable elements with a higher order interpolation for the displacement field in 2D and 3D examples.

Continuum damage mechanics is the basis of the crack growth strategy for the proposed fracture propagation technique. The strain softening models used for quasi-brittle materials favour spurious strain localization and ill-posedness of the boundary value problem if the damage variable only depends on the strain state at the point under consideration.

An integral-type non-local damage model associated to a characteristic length parameter is presented as a method to control the size of the fracture process zone and fully regularize the problem. Two examples are solved assessing the robustness of the model in front of changes in the spatial discretization.

Quasi-zero-thickness interface elements are formulated to represent discontinuities in the porous domain. A bilinear cohesive fracture model is used to describe its mechanical behaviour, and a formulation derived from the cubic law models the fluid flow through the crack.

Finally, a new methodology for the simulation of fracture propagation processes in saturated porous media is presented. The non-local damage model is used in conjunction with the interface elements to predict the degradation pattern of the domain and insert new fractures followed by remeshing. Fluid-driven fracture propagation examples in 2D and 3D are presented to illustrate the accuracy of the proposed technique.

Abstract

We present some advances in the formulation of the Particle Finite Element Method (PFEM) for solving complex fluid-structure interaction problems with free surface waves. In particular, we present extensions of the PFEM for the analysis of the interaction between a collection of bodies in water allowing for frictional contact conditions at the fluid-solid and solid-solid interfaces via mesh generation. An algorithm to treat bed erosion in free surface flows is also presented. Examples of application of the PFEM to solve a number of fluid-multibody interaction problems involving splashing of waves, large motions of floating and submerged bodies and bed erosion situations are given.

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.