The Fixed-Mesh ALE method applied to multiphysics problems using stabilized formulations
Visualitza/Obre
10.5821/dissertation-2117-94761
Inclou dades d'ús des de 2022
Cita com:
hdl:2117/94761
Càtedra / Departament / Institut
Universitat Politècnica de Catalunya. Departament de Resistència de Materials i Estructures a l'Enginyeria
Tipus de documentTesi
Data de defensa2011-01-14
EditorUniversitat Politècnica de Catalunya
Condicions d'accésAccés obert
Tots els drets reservats. Aquesta obra està protegida pels drets de propietat intel·lectual i
industrial corresponents. Sense perjudici de les exempcions legals existents, queda prohibida la seva
reproducció, distribució, comunicació pública o transformació sense l'autorització del titular dels drets
Abstract
The finite element method is a tool very often employed to deal with the numerical simulation
of multiphysics problems.Many times each of these problems can be attached to a subdomain
in space which evolves in time. Fixed grid methods appear in order to avoid the drawbacks of
remeshing in ALE (Arbitrary Lagrangian-Eulerian) methods when the domain undergoes very
large deformations. Instead of having one mesh attached to each of the subdomains, one has a
single mesh which covers the whole computational domain. Equations arising from the finite
element analysis are solved in an Eulerian manner in this background mesh. In this work we
present our particular approach to fixed mesh methods, which we call FM-ALE (Fixed-Mesh
ALE). Our main concern is to properly account for the advection of information as the domain
boundary evolves. To achieve this, we use an arbitrary Lagrangian-Eulerian framework, the
distinctive feature being that at each time step results are projected onto a fixed, background
mesh, that is where the problem is actually solved.We analyze several possibilities to prescribe
boundary conditions in the context of immersed boundary methods.
When dealing with certain physical problems, and depending on the finite element space
used, the standard Galerkin finite element method fails and leads to unstable solutions. The
variational multiscale method is often used to deal with this instability. We introduce a way
to approximate the subgrid scales on the boundaries of the elements in a variational twoscale
finite element approximation to flow problems. The key idea is that the subscales on the
element boundaries must be such that the transmission conditions for the unknown, split as its
finite element contribution and the subscale, hold. We then use the subscales on the element
boundaries to improve transmition conditions between subdomains by introducing the subgrid
scales between the interfaces in homogeneous domain interaction problems and at the interface
between the fluid and the solid in fluid-structure interaction problems. The benefits in each
case are respectively a stronger enforcement of the stress continuity in homogeneous domain
decomposition problems and a considerable improvement of the behaviour of the iterative
algorithm to couple the fluid and the solid in fluid-structure interaction problems.
We develop FELAP, a linear systems of equations solver package for problems arising from
finite element analysis. The main features of the package are its capability to work with symmetric
and unsymmetric systems of equations, direct and iterative solvers and various renumbering
techniques. Performance is enhanced by considering the finite element mesh graph
instead of the matrix graph, which allows to perform highly efficient block computations.
Descripció
Premi extraordinari doctorat curs 2010-2011, àmbit d’Enginyeria Civil
CitacióBaiges Aznar, J. The Fixed-Mesh ALE method applied to multiphysics problems using stabilized formulations. Tesi doctoral, UPC, Departament de Resistència de Materials i Estructures a l'Enginyeria, 2011. DOI 10.5821/dissertation-2117-94761. Disponible a: <http://hdl.handle.net/2117/94761>
GuardóDocument premiat
Dipòsit legalB. 10505-2013
Col·leccions
Fitxers | Descripció | Mida | Format | Visualitza |
---|---|---|---|---|
TJBA1de1.pdf | 9,331Mb | Visualitza/Obre |