Master of Science in Computational Mechanicshttp://hdl.handle.net/2099.1/83362020-05-25T02:30:50Z2020-05-25T02:30:50ZImplementation of conservative schemes in an edge-based finite element codeEspinoza Román, Héctorhttp://hdl.handle.net/2117/1221692018-10-11T01:59:51Z2018-10-10T13:48:23ZImplementation of conservative schemes in an edge-based finite element code
Espinoza Román, Héctor
In this work a novel edge-based ﬁnite element implementation applied to speciﬁc equations is presented. It contains a full description on how we obtained it for the diﬀusion equation, stabilized convection-diﬀusion equation
and stabilized Navier-Stokes equations. Additionally, classical benchmark problems are solved to show the capabilities of the new implementation. As the diﬀerential equations we are interested in represent conservation
statements, it would be desirable that the ﬁnite element approximation was exactly conservative (at least globally) independently of the mesh used. The present work revolves around that main objective. The initial available edge-based approximation is not totally conservative. Of course it becomes more and more conservative as the mesh is reﬁned. It has good h-convergence features and produces ’good solutions’ (in the sense that the method does not introduces spurious oscillations and is numerically stable). On the other hand, the edge-based approximation proposed is exactly globally conservative. Additionally it has good h-convergence features and produces ’good solutions’.
2018-10-10T13:48:23ZEspinoza Román, HéctorIn this work a novel edge-based ﬁnite element implementation applied to speciﬁc equations is presented. It contains a full description on how we obtained it for the diﬀusion equation, stabilized convection-diﬀusion equation
and stabilized Navier-Stokes equations. Additionally, classical benchmark problems are solved to show the capabilities of the new implementation. As the diﬀerential equations we are interested in represent conservation
statements, it would be desirable that the ﬁnite element approximation was exactly conservative (at least globally) independently of the mesh used. The present work revolves around that main objective. The initial available edge-based approximation is not totally conservative. Of course it becomes more and more conservative as the mesh is reﬁned. It has good h-convergence features and produces ’good solutions’ (in the sense that the method does not introduces spurious oscillations and is numerically stable). On the other hand, the edge-based approximation proposed is exactly globally conservative. Additionally it has good h-convergence features and produces ’good solutions’.Analysis of viscoelastic cell structures with dynamic topologyAlbo Guijarro, Santiagohttp://hdl.handle.net/2099.1/162262020-02-12T20:35:09Z2012-10-10T14:16:51ZAnalysis of viscoelastic cell structures with dynamic topology
Albo Guijarro, Santiago
[ANGLÈS] The present work proposes a way to model cell cytoskeleton using truss systems.
This allows large deformations and rotations to be handled in a natural way.
With this intention a framework has been developed which allows to use any
rheological law wished with very little e ort.
Classical models such as Kelvin-Voigt or Maxwell have been reviewed
analytically under standard experiments. The gathered information has
allowed us to propose a novel model that accounts for the observed growth of
cytoskeleton laments or, more usually called active lengthening. This model
behaves very similar to classical ones which means that it can explain the
observed
uid viscosity in in vivo experiments while giving a more satisfactory
explanation.
With dynamic topology a new concept has been introduced. This feature is
in fact relevant for the modelling of some morphogenetic movements where
some invasive cells replace other regions of the tissue modifying the global
look of the model.
Combining these two concepts yields a wide variety of new approaches to
follow in future related works.; [CASTELLÀ] En el presente trabajo se presenta una propuesta de modelización del
citoesqueleto celular mediante sistemas de barras. Estos permiten grandes
deformaciones y rotaciones de una forma natural. Con esta intención, se ha
desarrollado un código nuevo que permite la incorporación de cualquier modelo
reológico de forma sencilla.
Se han comprobado analíticamente los modelos clásicos de Kelvin-Voigt y
Maxwel bajo experimentos estándar, obteniendo una información que ha
permitido el desarrollo de un nuevo modelo que tiene en cuenta el crecimiento
observado del citoesqueleto. Además, este nuevo modelo se comporta de una
forma muy similar a los modelos clásicos, de forma que también puede explicar, y
de forma más satisfactoria, la viscosidad observada “in vivo”.
Adicionalmente, se introduce el nuevo concepto de la topología dinámica; de
gran importancia en el campo del modelado de movimientos morfogenéticos en
los que nuevas células reemplazan determinadas regiones de un tejido
modificando el aspecto global del modelo.
Como resultado de la combinación de estos dos conceptos, aparece una
amplia variedad de nuevos planteamientos que se deberán estudiar en futuros
trabajos.
Treball que, prèvia autorització de l'ETSECCPB, es va presentar simultàniament com a tesina de l'Enginyeria de Camins, Canals i Ports i com a projecte final del Master of Science in Computational Mechanics
2012-10-10T14:16:51ZAlbo Guijarro, Santiago[ANGLÈS] The present work proposes a way to model cell cytoskeleton using truss systems.
This allows large deformations and rotations to be handled in a natural way.
With this intention a framework has been developed which allows to use any
rheological law wished with very little e ort.
Classical models such as Kelvin-Voigt or Maxwell have been reviewed
analytically under standard experiments. The gathered information has
allowed us to propose a novel model that accounts for the observed growth of
cytoskeleton laments or, more usually called active lengthening. This model
behaves very similar to classical ones which means that it can explain the
observed
uid viscosity in in vivo experiments while giving a more satisfactory
explanation.
With dynamic topology a new concept has been introduced. This feature is
in fact relevant for the modelling of some morphogenetic movements where
some invasive cells replace other regions of the tissue modifying the global
look of the model.
Combining these two concepts yields a wide variety of new approaches to
follow in future related works.
[CASTELLÀ] En el presente trabajo se presenta una propuesta de modelización del
citoesqueleto celular mediante sistemas de barras. Estos permiten grandes
deformaciones y rotaciones de una forma natural. Con esta intención, se ha
desarrollado un código nuevo que permite la incorporación de cualquier modelo
reológico de forma sencilla.
Se han comprobado analíticamente los modelos clásicos de Kelvin-Voigt y
Maxwel bajo experimentos estándar, obteniendo una información que ha
permitido el desarrollo de un nuevo modelo que tiene en cuenta el crecimiento
observado del citoesqueleto. Además, este nuevo modelo se comporta de una
forma muy similar a los modelos clásicos, de forma que también puede explicar, y
de forma más satisfactoria, la viscosidad observada “in vivo”.
Adicionalmente, se introduce el nuevo concepto de la topología dinámica; de
gran importancia en el campo del modelado de movimientos morfogenéticos en
los que nuevas células reemplazan determinadas regiones de un tejido
modificando el aspecto global del modelo.
Como resultado de la combinación de estos dos conceptos, aparece una
amplia variedad de nuevos planteamientos que se deberán estudiar en futuros
trabajos.Modeling Thermal Turbulence Using Implicit Large Eddy SimulationHossain, Naimhttp://hdl.handle.net/2099.1/157822020-02-12T20:42:54Z2012-07-17T13:27:39ZModeling Thermal Turbulence Using Implicit Large Eddy Simulation
Hossain, Naim
A general description of a thermally coupled fluid flow is given by the incompressible Navier-Stokes equations coupled with the heat equation using Boussinesq approximation, whose mathematical structure is much well understood. A variational multiscale finite element approximation has been considered for the formulation of incompressible Navier-Stokes equation and heat equation. The complexity of these problems makes their numerical solution very difficult as the standard finite element method is unstable. In the incompressible Navier Stokes equations, two well known sources of numerical instabilities are the incompressibility constraint and the presence of the convective term.
Many stabilization techniques used nowadays are based on scale separation, splitting the unknown into a coarse part induced by the discretization of the domain and a fine subgrid part. The modeling of the subgrid scale and its influence leads to a modified coarse scale problem providing stability.
In convection-diffusion problem once global instabilities have been overcome by a stabilization method, there are still local oscillations near layers due to the lack of monotonicity of the method.
Shock capturing techniques are often employed to deal with them. Proper choice of stabilization and shock capturing techniques can eliminate the local instabilities near layers of convection-diffusion equation.
A very important issue of the formulation presented in this thermally coupled incompressible flow is the possibility to model turbulent flows. Some terms involving the velocity subgrid scale arise from the convective term in the Navier-Stokes equations which can be understood as the contribution from the Reynolds tensor of a LES approach and the contribution from the cross stress tensor. This opens the door of modeling thermal turbulence using LES automatically inherited by the formulation
used in this work.
Different classical benchmark problems are numerically solved in this thesis work for the convection-diffusion equation to show the capabilities of different combination of stabilization and shock capturing methods. In the case of thermally coupled incompressible flows some numerical and industrial examples are exhibited to check the performance of the different combination of stabilization
and shock capturing methods and to compare them. The objective is to conclude which method works better to approximate the exact solution and eliminate instabilities and local oscillations.
2012-07-17T13:27:39ZHossain, NaimA general description of a thermally coupled fluid flow is given by the incompressible Navier-Stokes equations coupled with the heat equation using Boussinesq approximation, whose mathematical structure is much well understood. A variational multiscale finite element approximation has been considered for the formulation of incompressible Navier-Stokes equation and heat equation. The complexity of these problems makes their numerical solution very difficult as the standard finite element method is unstable. In the incompressible Navier Stokes equations, two well known sources of numerical instabilities are the incompressibility constraint and the presence of the convective term.
Many stabilization techniques used nowadays are based on scale separation, splitting the unknown into a coarse part induced by the discretization of the domain and a fine subgrid part. The modeling of the subgrid scale and its influence leads to a modified coarse scale problem providing stability.
In convection-diffusion problem once global instabilities have been overcome by a stabilization method, there are still local oscillations near layers due to the lack of monotonicity of the method.
Shock capturing techniques are often employed to deal with them. Proper choice of stabilization and shock capturing techniques can eliminate the local instabilities near layers of convection-diffusion equation.
A very important issue of the formulation presented in this thermally coupled incompressible flow is the possibility to model turbulent flows. Some terms involving the velocity subgrid scale arise from the convective term in the Navier-Stokes equations which can be understood as the contribution from the Reynolds tensor of a LES approach and the contribution from the cross stress tensor. This opens the door of modeling thermal turbulence using LES automatically inherited by the formulation
used in this work.
Different classical benchmark problems are numerically solved in this thesis work for the convection-diffusion equation to show the capabilities of different combination of stabilization and shock capturing methods. In the case of thermally coupled incompressible flows some numerical and industrial examples are exhibited to check the performance of the different combination of stabilization
and shock capturing methods and to compare them. The objective is to conclude which method works better to approximate the exact solution and eliminate instabilities and local oscillations.An improved X-FEM solution to ensure normal stress continuity for two-phase flow problemsBozkus, Hayrullah Kerimhttp://hdl.handle.net/2099.1/157342020-02-12T20:42:54Z2012-07-13T13:39:43ZAn improved X-FEM solution to ensure normal stress continuity for two-phase flow problems
Bozkus, Hayrullah Kerim
In this thesis, starting from the foundations of the Theory of Classical Finite Elements Method, The basic principles of Extended Finite Elements Method (X-FEM) are Explained. Why X-FEM takes place in many applications in industry is also emphasized.
2012-07-13T13:39:43ZBozkus, Hayrullah KerimIn this thesis, starting from the foundations of the Theory of Classical Finite Elements Method, The basic principles of Extended Finite Elements Method (X-FEM) are Explained. Why X-FEM takes place in many applications in industry is also emphasized.Numerical Approximation of Filtration Processes through Porous MediaAhmed, Raheelhttp://hdl.handle.net/2099.1/157282019-01-24T11:37:16Z2012-07-13T12:06:58ZNumerical Approximation of Filtration Processes through Porous Media
Ahmed, Raheel
In this thesis, we studied numerical methods for the coupling of free fluid flow with porous medium flow. The free fluid flow is modelled by the Stokes equations while the flow in the porous medium is modelled by Darcy’s law. Appropriate conditions are imposed at the interface between the two regions. The weak formulation of the problem is based on mixed-formulation for Stokes and
on a primal-mixed formulation for Darcy equation, incorporating in a natural way the interface conditions. The finite element discretization of the problem leads to large, sparse and ill-conditioned algebraic system to be solved for velocities in both domains, Stokes pressure and piezometric head in
porous domain. The system is reduced to interface systems for the normal velocity and piezometric head by a Schur complement approach. We present numerical results for several solution methods based on different preconditioning techniques for the solution of the interface systems. We study the effectiveness of the preconditioners with respect to mesh refinement and physical parameters.
An application to cross-flow membranes has been considered. Finally, we also assess the numerical accuracy of an uncoupled algorithm for transient problem, which uses different time steps in the Stokes and in the Darcy domains.
2012-07-13T12:06:58ZAhmed, RaheelIn this thesis, we studied numerical methods for the coupling of free fluid flow with porous medium flow. The free fluid flow is modelled by the Stokes equations while the flow in the porous medium is modelled by Darcy’s law. Appropriate conditions are imposed at the interface between the two regions. The weak formulation of the problem is based on mixed-formulation for Stokes and
on a primal-mixed formulation for Darcy equation, incorporating in a natural way the interface conditions. The finite element discretization of the problem leads to large, sparse and ill-conditioned algebraic system to be solved for velocities in both domains, Stokes pressure and piezometric head in
porous domain. The system is reduced to interface systems for the normal velocity and piezometric head by a Schur complement approach. We present numerical results for several solution methods based on different preconditioning techniques for the solution of the interface systems. We study the effectiveness of the preconditioners with respect to mesh refinement and physical parameters.
An application to cross-flow membranes has been considered. Finally, we also assess the numerical accuracy of an uncoupled algorithm for transient problem, which uses different time steps in the Stokes and in the Darcy domains.Simultaneous untangling and smoothing of hexahedral meshnesRivas Guerra, César Augustohttp://hdl.handle.net/2099.1/123632020-02-12T20:42:54Z2011-06-30T10:42:38ZSimultaneous untangling and smoothing of hexahedral meshnes
Rivas Guerra, César Augusto
Currently, there is not a general method such that any given geometry can generate
a mesh with elements of hexahedral type. However, there are several methods used to create the numerical discretization for certain types of geometries. Unfortunately,
these methods could generate meshes with highly distorted elements and in some cases
the mesh obtained may include tangled elements. Therefore, it is of most importance
to develop a procedure that could smooth and untangle hexahedral meshes.
This work will provide a method that improves the quality of unstructured meshes
and, if required, untangle the inverted elements by the minimization of a smoothed
objective function. This objective function is based on the shape quality index of the
elements or in the conditioning number of the shape matrix. To illustrate the applica-
tion of the proposed smoother, several example of tangled meshes are presented, show-ing how the smoother untangles and smoothes quadrilateral and hexahedral meshes.
A comparison of the performance between several minimization methods is presented.
Finally, the robustness of smoother is compared to one of the most used smoothing
methods.
2011-06-30T10:42:38ZRivas Guerra, César AugustoCurrently, there is not a general method such that any given geometry can generate
a mesh with elements of hexahedral type. However, there are several methods used to create the numerical discretization for certain types of geometries. Unfortunately,
these methods could generate meshes with highly distorted elements and in some cases
the mesh obtained may include tangled elements. Therefore, it is of most importance
to develop a procedure that could smooth and untangle hexahedral meshes.
This work will provide a method that improves the quality of unstructured meshes
and, if required, untangle the inverted elements by the minimization of a smoothed
objective function. This objective function is based on the shape quality index of the
elements or in the conditioning number of the shape matrix. To illustrate the applica-
tion of the proposed smoother, several example of tangled meshes are presented, show-ing how the smoother untangles and smoothes quadrilateral and hexahedral meshes.
A comparison of the performance between several minimization methods is presented.
Finally, the robustness of smoother is compared to one of the most used smoothing
methods.Approximation of the inductionless MHD system with finite element techniquesPlanas Badenas, Ramonhttp://hdl.handle.net/2099.1/123622020-05-04T01:54:26Z2011-06-30T10:33:50ZApproximation of the inductionless MHD system with finite element techniques
Planas Badenas, Ramon
In this work, a stabilized formulation to solve the inductionless magnetohydrodynamic
(MHD) problem using the finite element method is presented. The important feature of this formulation resides in the design of the stabilization terms, which serve several purposes.
First, convective dominated flows in the Navier-Stokes equations can be dealt with. Second, there is no need to use interpolation spaces subject to an inf-sup condition both for the pairs u-p and j- and therefore linear interpolation spaces can be used. Finally, this formulation allows to deal with flows with high values of the Hartmann number, that is, flows where the electromagnetic forces are much higher than the viscous forces.
2011-06-30T10:33:50ZPlanas Badenas, RamonIn this work, a stabilized formulation to solve the inductionless magnetohydrodynamic
(MHD) problem using the finite element method is presented. The important feature of this formulation resides in the design of the stabilization terms, which serve several purposes.
First, convective dominated flows in the Navier-Stokes equations can be dealt with. Second, there is no need to use interpolation spaces subject to an inf-sup condition both for the pairs u-p and j- and therefore linear interpolation spaces can be used. Finally, this formulation allows to deal with flows with high values of the Hartmann number, that is, flows where the electromagnetic forces are much higher than the viscous forces.Numerical simulation of the dynamics of fluid membranesGrosjean, Laurencehttp://hdl.handle.net/2099.1/83802020-02-12T20:42:54Z2010-01-18T15:37:11ZNumerical simulation of the dynamics of fluid membranes
Grosjean, Laurence
The goal of this project is to explore the mechanics of lipid fluid membranes as
found in biological and made-man systems through continuum models and numerical
simulations. Traditionally, the focus has been on the equilibrium configurations of
vesicles through minimization of the curvature energy subject to constraints. Here,
the goal is to describe the time-evolution of out-of-equilibrium vesicle configurations,
which are of relevance in biological systems. Towards this goal, an accurate description
of the dissipative mechanisms is crucial, in particular the viscous dissipation
induced by the 2D flow of lipids on the deforming surface that describes a vesicle [1].
The resulting equations can only be solved analytically in very simple settings. So the
problem is solved numerically using a B-Spline description of the membrane vesicle.
The dynamics are described using two types of viscosity: the L2 or Willmore viscosity
and the inner flow viscosity. By comparing the evolution in time of the two systems, it
is stated that the dynamics are clearly different. It is found that one describes better
the physics of the system.
2010-01-18T15:37:11ZGrosjean, LaurenceThe goal of this project is to explore the mechanics of lipid fluid membranes as
found in biological and made-man systems through continuum models and numerical
simulations. Traditionally, the focus has been on the equilibrium configurations of
vesicles through minimization of the curvature energy subject to constraints. Here,
the goal is to describe the time-evolution of out-of-equilibrium vesicle configurations,
which are of relevance in biological systems. Towards this goal, an accurate description
of the dissipative mechanisms is crucial, in particular the viscous dissipation
induced by the 2D flow of lipids on the deforming surface that describes a vesicle [1].
The resulting equations can only be solved analytically in very simple settings. So the
problem is solved numerically using a B-Spline description of the membrane vesicle.
The dynamics are described using two types of viscosity: the L2 or Willmore viscosity
and the inner flow viscosity. By comparing the evolution in time of the two systems, it
is stated that the dynamics are clearly different. It is found that one describes better
the physics of the system.