Approximate Dirichlet boundary conditions in time-evolving physical domains
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hdl:2117/103215
Correu electrònic de l'autorguilli_arregui_92hotmail.com
Tipus de documentProjecte Final de Màster Oficial
Data2016-06-23
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Reconeixement 3.0 Espanya
Abstract
In many coupled fluid-structure problems of practical interest the domain of at least one of
the problems evolves in time. The most often applied approach to deal with such motion
in numerical methods is the use of the Arbitrary Eulerian-Lagrangian (ALE) framework.
However, the use of a pure fixed-mesh could allow us to get rid of choosing the arbitrary
mesh velocity and is often more adapted for fluid motion. Nevertheless, several other
problems arise from such a strategy when applied to the finite element method (FEM),
especially regarding the application of Dirichlet boundary conditions (BCs).
The usual strategy to prescribe Dirichlet BCs in FEM is to define the boundary of the
domain by placing nodes and facets on it, which allows us to strongly impose the condition
by defining the unknown as such in the given nodes. However, it is quite straightforward
to see that if a fixed-mesh strategy is to be used on, for example, a solid moving domain
inside a fluid, non-matching or non-conforming grids will appear at every time step of
calculation. In this cases, the boundary geometry intersects the boundary cells in an arbitrary
way. To solve such a problem several techniques have been developed, such as the
immersed boundary method, the penalty method, Nitsche’s method, the use of Lagrange
multipliers and other techniques that combine several of these strategies. These methods
impose the BCs in an approximate way once the discretization has been carried out, either
by modifying the differential operators near the interface (in finite differences) or by
modifying the unknowns near the interface.
In this work we describe such numerical techniques for approximating Dirichlet BCs
for the transient incompressible Navier-Stokes (N-S) equations. Some of these techniques
have been programmed on FEMUSS (Finite Element Method Using Subscale Stabilitzation),
one of the multiphysics Fortran code used at the International Centre for Numerical
Methods in Engineering (CIMNE) and we applied them to study the flow of fluids around
time-evolving prescribed solids.
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MasterThesis_GuillermoArregui.pdf | 4,919Mb | Visualitza/Obre |