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101 |
Pseudoparabolinės lygties su nelokaliosiomis integralinėmis sąlygomis sprendimas baigtinių skirtumų metodu / Solution of a pseudoparabolic equation with nonlocal integral conditions by the finite difference methodJachimavičienė, Justina 20 February 2013 (has links)
Disertacijoje išnagrinėta trečiosios eilės vienmatė pseudoparabolinė lygtis su dviejų tipų nelokaliosiomis sąlygomis. Šiems uždaviniams spręsti sudarytos skirtuminės schemos, kurių stabilumas tiriamas, taikant skirtuminių operatorių su nelokaliosiomis sąlygomis spektro struktūrą. Trečiosios eilės vienmatėms ir dvimatėms pseudoparabolinėms lygtims su integralinėmis sąlygomis sudarytos ir išnagrinėtos padidinto tikslumo skirtuminės schemos. Išnagrinėta dvimatė pseudoparabolinė lygtis su nelokaliosiomis integralinėmis sąlygomis viena koordinačių kryptimi. Tokiam uždaviniui spręsti pritaikytas ir išnagrinėtas lokaliai vienmatis metodas, ištirtos šio metodo stabilumo sąlygos. Taip pat išnagrinėtos: trisluoksnės skirtuminės schemos vienmatei pseudoparabolinei lygčiai su įvairiomis, taip pat ir nelokaliosiomis, sąlygomis; trisluoksnių išreikštinių skirtuminių schemų stabilumo sąlygos. / The thesis analyzes the third-order one-dimensional pseudoparabolic equations with two types of nonlocal conditions. The stability of difference schemes for this problem was studied using the analysis of the spectrum structure of a difference operator with nonlocal conditions. The analysis of the increased accuracy difference schemes for third-order one-dimensional and two-dimensional pseudoparabolic equations with integral conditions has been made. The thesis considers a two-dimensional pseudoparabolic equation with nonlocal integral conditions in one coordinate direction. This problem was solved by a locally one-dimensional method. The stability of a difference scheme has been investigated based on the spectrum structure. The doctoral disertation investigates three-layer difference schemes for one-dimensional pseudoparabolic equations with various, including nonlocal, conditions. Also, the conditions for the stability of three-layer explicit difference schemes have been explored.
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102 |
Credit Value Adjusted Real Options Based Valuation of Multiple-Exercise Government Guarantees for Infrastructure ProjectsNaji Almassi, Ali 24 July 2013 (has links)
Public-Private-Partnership (P3) is gaining momentum as the delivery method for the development of public infrastructure. These projects, however, are exposed to economic risks. If the private parties are not comfortable with the level of the risks, they would not participate in the project and, as a result, the infrastructure will most likely not be realized. As an incentive for participation in the P3 project, private parties are sometimes offered guarantees against unfavorable economic risks. Therefore, the valuation of these guarantees is essential for deciding whether or not to participate in the project.
While previous works focused on the valuation of guarantees, the incorporation of credit risk in the value of the P3 projects and the guarantees has been neglected. The effect of credit risk can be taken into account by using the rigorous Credit Value Adjustment method (CVA). CVA is a computationally demanding method that the valuation methods currently in the literature are not capable of handling.
This research offers a novel approach for the valuation of guarantees and P3 projects which is computationally superior to the existing methods. Because of this computational efficiency, CVA can be implemented to account for credit risk. For the development of this method, a continuous stochastic differential equation (SDE) is derived from the forecasted curve of an economic risk. Using the SDE, the partial differential equation (PDE) governing the value of the guarantees will be derived. Then, the PDE will be solved using Finite Difference Method (FDM). A new feature for this method is that it obtains exercise strategies for the Australian guarantees.
The present work extends the literature by providing a valuation method for the cases that multiple risks affect P3 projects. It also presents an approach for the valuation of the Asian style guarantee, a contract which reimburses the private party based on the average of risk factor. Finally, a hypothetical case study illustrates the implementation of the FDM-based valuation method and CVA to obtain the value of the P3 project and the guarantees adjusted for the counterparty credit risk.
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103 |
Credit Value Adjusted Real Options Based Valuation of Multiple-Exercise Government Guarantees for Infrastructure ProjectsNaji Almassi, Ali 24 July 2013 (has links)
Public-Private-Partnership (P3) is gaining momentum as the delivery method for the development of public infrastructure. These projects, however, are exposed to economic risks. If the private parties are not comfortable with the level of the risks, they would not participate in the project and, as a result, the infrastructure will most likely not be realized. As an incentive for participation in the P3 project, private parties are sometimes offered guarantees against unfavorable economic risks. Therefore, the valuation of these guarantees is essential for deciding whether or not to participate in the project.
While previous works focused on the valuation of guarantees, the incorporation of credit risk in the value of the P3 projects and the guarantees has been neglected. The effect of credit risk can be taken into account by using the rigorous Credit Value Adjustment method (CVA). CVA is a computationally demanding method that the valuation methods currently in the literature are not capable of handling.
This research offers a novel approach for the valuation of guarantees and P3 projects which is computationally superior to the existing methods. Because of this computational efficiency, CVA can be implemented to account for credit risk. For the development of this method, a continuous stochastic differential equation (SDE) is derived from the forecasted curve of an economic risk. Using the SDE, the partial differential equation (PDE) governing the value of the guarantees will be derived. Then, the PDE will be solved using Finite Difference Method (FDM). A new feature for this method is that it obtains exercise strategies for the Australian guarantees.
The present work extends the literature by providing a valuation method for the cases that multiple risks affect P3 projects. It also presents an approach for the valuation of the Asian style guarantee, a contract which reimburses the private party based on the average of risk factor. Finally, a hypothetical case study illustrates the implementation of the FDM-based valuation method and CVA to obtain the value of the P3 project and the guarantees adjusted for the counterparty credit risk.
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104 |
Implementation Of Turbulence Models Into A Navier-stokes SolverMusta, Mustafa Nail 01 September 2004 (has links) (PDF)
In order to handle turbulent flow problems, one equation turbulence models are implemented in to a previously developed explicit, Reynolds averaged Navier-Stokes solver. Discretization of Navier-Stokes solver is based on cell-vertex finite volume formulation combined with single step Lax-Wendroff numerical method which is second order accurate in space. Turbulent viscosity is calculated by using one equation Spalart-Allmaras and Baldwin-Barth turbulence transport equations. For the discretization of Spalart-Allmaras and Baldwin-Barth equations, both finite volume scheme which is used for Navier-Stokes equation in this work and explicit finite difference discretization method are used.
In order to increase the convergence rate of the solver, local time stepping technique is applied. Stabilization of non-physical oscillations resulting from the numerical scheme is maintained by adding second and fourth order artificial smoothing terms.
Three test cases are considered. In order to validate the accuracy of the Navier-Stokes solver, solver is tested over a laminar flat plate. The results are compared with analytical solutions. Later, in order to check the performance of the turbulence models, turbulent flow over flat plate and turbulent transonic flow over NACA-0012 airfoil are handled. For turbulent flow over flat plate obtained results are compared with analytical and empirical solutions, whereas for transonic turbulent flow obtained results are compared with numerical and experimental solutions.
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105 |
Mixed quantum and classical simulation techniques for mapping electron transfer in proteinsWallrapp, Frank 04 April 2011 (has links)
El
objetivo
de
esta
tesis
se
centra
en
el
estudio
de
la
transferencia
de
electrones
(ET),
una
de
las
reacciones
más
simples
y
cruciales
en
bioquímica.
Para
dichos
procesos,
obtener
información
directa
de
los
factores
que
lo
promueves,
asi
como
del
camino
de
transferencia
electronica,
no
es
una
tarea
trivial.
Dicha
información
a
un
nivel
de
conocimiento
detallado
atómico
y
electrónico,
sin
embargo,
es
muy
valiosa
en
términos
de
una
mejor
comprensión
del
ciclo
enzimático,
que
podría
conducir,
por
ejemplo,
a
un
diseño
más
eficaz
de
inhibidores.
El
objetivo
principal
de
esta
tesis
es
el
desarrollo
de
una
metodología
para
el
estudio
cuantitativo
de
la
ET
en
los
sistemas
biológicos.
En
este
sentido,
hemos
desarrollado
un
nuevo
método
para
obtener
el
camino
de
transferencia
electrónico,
llamado
QM/MM
e-‐
Pathway,
que
se
puede
aplicar
en
sistemas
complejos
con
ET
de
largo
alcance.
El
método
se
basa
en
una
búsqueda
sucesiva
de
residuos
importantes
para
la
ET,
utilizando
la
modificación
de
la
región
quantica
en
métodos
mixtos
QM/MM,
y
siguiendo
la
evolución
de
la
densidad
de
espín
dentro
de
la
zona
de
transferencia.
Hemos
demostrado
la
utilidad
y
la
aplicabilidad
del
algoritmo
en
el
complejo
P450cam/Pdx,
identificando
el
papel
clave
de
la
Arg112
(en
P450cam)
y
del
Asp48
(en
Pdx),
ambos
conocidos
en
la
literatura.
Además
de
obtener
caminos
de
ET,
hemos
cuantificado
su
importancia
en
términos
del
acoplamiento
electrónico
entre
el
dador
y
aceptor
para
los
diferentes
caminos.
En
este
sentido,
se
realizaron
dos
estudios
de
la
influencia
del
solvente
y
de
la
temperatura
en
el
acoplamiento
electrónico
para
sistemas
modelo
oligopéptidos.
Ambos
estudios
revelaron
que
los
valores
del
acoplamiento
electrónico
fluctúan
fuertemente
a
lo
largo
de
las
trayectorias
de
dinámica
molecular
obtenidas,
y
el
mecanismo
de
transferencia
de
electrones
se
ve
ampliamente
afectado
por
el
espacio
conformacional
del
sistema.
La
combinación
del
QM/MM
e-‐pathway
y
de
los
cálculos
de
acoplamiento
electronico
fueron
utilizados
finalmente
para
investigar
la
ET
en
el
complejo
CCP/Cytc.
Nuestros
hallazgos
indican
el
papel
fundamental
del
Trp191
en
localizar
un
estadio
intermedio
para
la
transferencia
electronica,
así
como
el
camino
ET
principal
que
incluye
Ala194,
Ala193,
Gly192
y
Trp191.
Ambos
hallazgos
fueron
confirmados
a
través
de
la
literatura.
Los
resultados
obtenidos
para
el
muestro
de
manios
de
ET,
junto
con
su
evaluación
a
través
de
cálculos
de
acoplamiento
electrónico,
sugieren
un
enfoque
sencillo
y
prometedor
para
investigar
ET
de
largo
alcance
en
proteínas. / The
focus
of
this
PhD
thesis
lies
on
electron
transfer
(ET)
processes,
belonging
to
the
simplest
but
most
crucial
reactions
in
biochemistry.
Getting
direct
information
of
the
forces
driving
the
process
and
the
actual
electron
pathway
is
not
a
trivial
task.
Such
atomic
and
electronic
detailed
information,
however,
is
very
valuable
in
terms
of
a
better
understanding
of
the
enzymatic
cycle,
which
might
lead,
for
example,
to
more
efficient
protein
inhibitor
design.
The
main
objective
of
this
thesis
was
the
development
of
a
methodology
for
the
quantitative
study
of
ET
in
biological
systems.
In
this
regard,
we
developed
a
novel
approach
to
map
long-‐range
electron
transfer
pathways,
called
QM/MM
e-‐Pathway.
The
method
is
based
on
a
successive
search
for
important
ET
residues
in
terms
of
modifying
the
QM
region
following
the
evolution
of
the
spin
density
of
the
electron
(hole)
within
a
given
transfer
region.
We
proved
the
usefulness
and
applicability
of
the
algorithm
on
the
P450cam/Pdx
complex,
indicating
the
key
role
of
Arg112
of
P450cam
and
Asp48
of
Pdx
for
its
ET
pathway,
both
being
known
to
be
important
from
the
literature.
Besides
only
identifying
the
ET
pathways,
we
further
quantified
their
importance
in
terms
of
electronic
coupling
of
donor
and
acceptor
incorporating
the
particular
pathway
residues.
Within
this
regard,
we
performed
two
systematic
evaluations
of
the
underlying
reasons
for
the
influence
of
solvent
and
temperature
onto
electronic
coupling
in
oligopeptide
model
systems.
Both
studies
revealed
that
electronic
coupling
values
strongly
fluctuate
throughout
the
molecular
dynamics
trajectories
obtained,
and
the
mechanism
of
electron
transfer
is
affected
by
the
conformational
space
the
system
is
able
to
occupy.
Combining
both
ET
mapping
and
electronic
coupling
calculations,
we
finally
investigated
the
electron
transfer
in
the
CcP/Cytc
complex.
Our
findings
indicate
the
key
role
of
Trp191
being
the
bridge-‐localized
state
of
the
ET
as
well
as
the
main
pathway
consisting
of
Ala194,
Ala193,
Gly192
and
Trp191
between
CcP
and
Cytc.
Both
findings
were
confirmed
through
the
literature.
Moreover,
our
calculations
on
several
snapshots
state
a
nongated
ET
mechanism
in
this
protein
complex.
The
methodology
developed
along
this
thesis,
mapping
ET
pathways
together
with
their
evaluation
through
electronic
coupling
calculations,
suggests
a
straightforward
and
promising
approach
to
investigate
long-‐range
ET
in
proteins.
|
106 |
Experimental kinetics studies and wavelet-based modelling of a reactive crystallisation systemUtomo, Johan January 2009 (has links)
This thesis has made two significant contributions to the field of reactive crystallisation. First, new data from batch cooling crystallisation and semi-batch reactive crystallisation experiments of mono-ammonium phosphate (MAP) were obtained to describe the key factors that influence crystal nucleation and growth rates, crystal size distribution (CSD), and crystal shape. The second contribution is the development of a numerical scheme for solving the population balance equations, which can be used to describe the evolution of CSD during the crystallisation process. This scheme combines the finite difference method with a wavelet method, and is the first reported application of this approach for crystallisation modelling and simulation. / Experiments into the batch cooling crystallisation of MAP were conducted both with and without seed crystals. The effects of key factors such as cooling rate, initial level of supersaturation and seeding technique, including seed concentration and seed size, on the real time supersaturation, final CSD, crystal yield and crystal shape were investigated. It was found that a seed concentration of 20-30% effectively suppressed nucleation. The growth and nucleation rate were estimated by using an isothermal seeded batch approach and their parameters were calculated by non-linear optimisation techniques. / The second series of experiments involved the semi-batch reactive crystallisation of MAP. Both single-feed and dual-feed systems were investigated. In the single-feed arrangement, an ammonia solution was fed into a charge of phosphoric acid. In the dual-feed system, phosphoric acid and ammonia solution were fed into a charge of saturated MAP solution. The molar ratio of the reactants, initial supersaturation, presence or absence of seed crystals, initial MAP concentration, reactants’ flow rate, feeding time and stirring speed were varied, and the effects upon the real time supersaturation, final CSD, crystal yield, crystal shape and solution temperature were measured. X-ray diffraction analysis showed that MAP can be produced in both the single-feed and dual-feed arrangements. For the single feed system, the N/P mole ratio controlled the degree of reaction and the CSD of the product. Di-ammonium phosphate (DAP) was not be observed in the single-feed system due to its high solubility. In the dual-feed system, a seeded solution with slow feed addition, moderate stirring speed and a low initial supersaturation provided the most favourable conditions for generating a desirable supersaturation profile, and thus obtaining a product with good CSD and crystal shape. / A comparative numerical study was undertaken in order to evaluate the existing numerical schemes for solving the population balance equations (PBE) that describe crystallisation. Several analytical solutions to the PBE were used to benchmark the following numerical schemes: Upwind Finite Difference, Biased Upwind Finite Difference, Orthogonal Collocation with Finite Elements, and Wavelet Orthogonal Collocation. The Wavelet Finite Difference (WFD) method has been applied here for the first time for solving PBE problems. The WFD scheme was adapted to solve the batch cooling and the semi-batch reactive crystallisation models, and the solutions were validated against experimental data that we obtained. / In summary, the experimental data provide an improved understanding of MAPreaction and crystallisation mechanisms. The adaptability of the WFD method has beendemonstrated validating the two crystallisation systems, and this should help extendthe application of wavelet-based solutions beyond crystallisation processes and intomore diverse areas of chemical engineering.
|
107 |
An?lise de modelo conceitual de simula??o de fluxo hidrogeol?gico por meio do m?todo das diferen?as finitas no munic?pio de Te?filo Otoni - MGAguiar, Victor Luiz Batista 15 March 2017 (has links)
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Previous issue date: 2017 / A crescente demanda pela utiliza??o de recursos h?dricos em nossa sociedade faz com que seja necess?ria a amplia??o dos meios de capta??o de ?gua. As ?guas subterr?neas surgem como alternativa ? capta??o convencional, tendo em vista que o armazenamento da ?gua nas camadas inferiores do solo garanta a manuten??o da qualidade deste recurso, uma vez que passam por processos naturais de filtra??o. Nesse sentido, a caracteriza??o dos sistemas aqu?feros por meio de modelagem matem?tica surge como ferramenta de aux?lio na compreens?o do fluxo subterr?neo local. A presente pesquisa tem como principal objetivo analisar o comportamento hidrogeol?gico do munic?pio de Te?filo Otoni - MG, com base em simula??es oriundas de modelos conceituais, pelo m?todo das diferen?as finitas. Por meio de simula??o de propriedades
influentes no transporte h?drico como taxa de recarga, vaz?o de bombeamento de po?os e condutividade hidr?ulica, foi poss?vel observar as varia??es nos valores m?ximos e m?nimos de carga hidr?ulica em pontos discretizados nos limites do modelo conceitual proposto, auxiliando assim no entendimento dos resultados obtidos. / Disserta??o (Mestrado Profissional) ? Programa de P?s-Gradua??o em Tecnologia, Sa?de e Sociedade, Universidade Federal dos Vales do Jequitinhonha e Mucuri, 2017. / The growing demand for the use of water resources in our society makes it necessary to expand the means of abstraction of water. Groundwater emerges as an alternative to conventional abstraction, owing to the storage of water in the lower layers of the soil ensures the maintenance of the quality of this resource, since they undergo natural filtration processes. In this sense, the characterization of the aquifer systems through mathematical modeling appears as a tool to aid in the understanding of the local underground flow. The present research has as main objective to analyze the hydrogeological behavior of Te?filo Otoni - MG, based on simulations derived from conceptual models, by the finite difference method. By means of simulation of influent properties in the water transport as recharge rate, well pumping rate and hydraulic conductivity
it was possible to observe the variations in the maximum and minimum values of hydraulic head in discretized points within the limits of the proposed conceptual model, thus helping in the understanding of the results obtained.
|
108 |
Formação de nanopadrões em superfícies por sputtering iônico: Estudo numérico da equação anisotrópica amortecida de Kuramoto-Sivashinsky. / Nano-patterning of surfaces by ion beam sputtering: numerical study of the anisotropic damped Kuramoto-Sivashinsky equation.Eduardo Vitral Freigedo Rodrigues 24 July 2015 (has links)
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Apresenta-se uma abordagemnumérica para ummodelo que descreve a formação
de padrões por sputtering iônico na superfície de ummaterial. Esse processo é responsável
pela formação de padrões inesperadamente organizados, como ondulações, nanopontos e
filas hexagonais de nanoburacos. Uma análise numérica de padrões preexistentes é proposta
para investigar a dinâmica na superfície, baseada em ummodelo resumido em uma equação
anisotrópica amortecida de Kuramoto-Sivashinsky, em uma superfície bidimensional com
condições de contorno periódicas. Apesar de determinística, seu caráter altamente não-linear
fornece uma rica gama de resultados, sendo possível descrever acuradamente diferentes
padrões. Umesquema semi implícito de diferenças finitas com fatoração no tempo é aplicado
na discretização da equação governante. Simulações foram realizadas com coeficientes
realísticos relacionados aos parâmetros físicos (anisotropias, orientação do feixe, difusão). A
estabilidade do esquema numérico foi analisada por testes de passo de tempo e espaçamento
de malha, enquanto a verificação do mesmo foi realizada pelo Método das Soluções Manufaturadas.
Ondulações e padrões hexagonais foram obtidos a partir de condições iniciais
monomodais para determinados valores do coeficiente de amortecimento, enquanto caos
espaço-temporal apareceu para valores inferiores. Os efeitos anisotrópicos na formação de
padrões foramestudados, variando o ângulo de incidência. / A numerical approach is presented for amodel describing the pattern formation by ion
beam sputtering on a material surface. This process is responsible for the appearance of unexpectedly
organized patterns, such as ripples, nanodots, and hexagonal arrays of nanoholes.
A numerical analysis of preexisting patterns is proposed to investigate surface dynamics,
based on a model resumed in an anisotropic damped Kuramoto-Sivashinsky equation, in a
two dimensional surface with periodic boundary conditions. While deterministic, its highly
nonlinear character gives a rich range of results, making it possible to describe accurately
different patterns. A finite-difference semi-implicit time splitting scheme is employed on the
discretization of the governing equation. Simulations were conducted with realistic coefficients
related to physical parameters (anisotropies, beam orientation, diffusion). The stability
of the numerical scheme is analyzed with time step and grid spacing tests for the pattern
evolution, and the Method ofManufactured Solutions has been used to verify the scheme.
Ripples and hexagonal patterns were obtained from amonomodal initial condition for certain
values of the damping coefficient, while spatiotemporal chaos appeared for lower values. The
anisotropy effects on pattern formation were studied, varying the angle of incidence.
|
109 |
Formação de nanopadrões em superfícies por sputtering iônico: Estudo numérico da equação anisotrópica amortecida de Kuramoto-Sivashinsky. / Nano-patterning of surfaces by ion beam sputtering: numerical study of the anisotropic damped Kuramoto-Sivashinsky equation.Eduardo Vitral Freigedo Rodrigues 24 July 2015 (has links)
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Apresenta-se uma abordagemnumérica para ummodelo que descreve a formação
de padrões por sputtering iônico na superfície de ummaterial. Esse processo é responsável
pela formação de padrões inesperadamente organizados, como ondulações, nanopontos e
filas hexagonais de nanoburacos. Uma análise numérica de padrões preexistentes é proposta
para investigar a dinâmica na superfície, baseada em ummodelo resumido em uma equação
anisotrópica amortecida de Kuramoto-Sivashinsky, em uma superfície bidimensional com
condições de contorno periódicas. Apesar de determinística, seu caráter altamente não-linear
fornece uma rica gama de resultados, sendo possível descrever acuradamente diferentes
padrões. Umesquema semi implícito de diferenças finitas com fatoração no tempo é aplicado
na discretização da equação governante. Simulações foram realizadas com coeficientes
realísticos relacionados aos parâmetros físicos (anisotropias, orientação do feixe, difusão). A
estabilidade do esquema numérico foi analisada por testes de passo de tempo e espaçamento
de malha, enquanto a verificação do mesmo foi realizada pelo Método das Soluções Manufaturadas.
Ondulações e padrões hexagonais foram obtidos a partir de condições iniciais
monomodais para determinados valores do coeficiente de amortecimento, enquanto caos
espaço-temporal apareceu para valores inferiores. Os efeitos anisotrópicos na formação de
padrões foramestudados, variando o ângulo de incidência. / A numerical approach is presented for amodel describing the pattern formation by ion
beam sputtering on a material surface. This process is responsible for the appearance of unexpectedly
organized patterns, such as ripples, nanodots, and hexagonal arrays of nanoholes.
A numerical analysis of preexisting patterns is proposed to investigate surface dynamics,
based on a model resumed in an anisotropic damped Kuramoto-Sivashinsky equation, in a
two dimensional surface with periodic boundary conditions. While deterministic, its highly
nonlinear character gives a rich range of results, making it possible to describe accurately
different patterns. A finite-difference semi-implicit time splitting scheme is employed on the
discretization of the governing equation. Simulations were conducted with realistic coefficients
related to physical parameters (anisotropies, beam orientation, diffusion). The stability
of the numerical scheme is analyzed with time step and grid spacing tests for the pattern
evolution, and the Method ofManufactured Solutions has been used to verify the scheme.
Ripples and hexagonal patterns were obtained from amonomodal initial condition for certain
values of the damping coefficient, while spatiotemporal chaos appeared for lower values. The
anisotropy effects on pattern formation were studied, varying the angle of incidence.
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Estudo comparativo de formulações do MEC para análise da interação estaca-solo / Comparative study of BEM formulations for the analysis of pile-soil interactionAlessandra Kiyoko da Rosa 01 November 2013 (has links)
Para uma análise mais exata do sistema estrutural, é necessário um estudo do comportamento interativo entre as diversas partes que o compõe, entre eles, destaca-se a interação entre os elementos de fundação e o maciço de solos. Neste trabalho foram desenvolvidas formulações numéricas para a análise da interação estaca-solo via acoplamento entre diferentes métodos numéricos: método dos elementos de contorno, método dos elementos finitos e método das diferenças finitas. As estacas podem estar submetidas a carregamentos horizontais, verticais e momentos aplicados em seu topo. Nestas formulações foram utilizadas, além das equações integrais de deslocamentos, as equações de suas derivadas, levando a um grau maior de singularidade, porém permitindo a adoção de aproximações mais refinadas para os deslocamentos e tensões ao longo da estaca. Todos os deslocamentos e suas derivadas referentes à estaca foram compatibilizados com os correspondentes do solo. Desenvolvidas as formulações, feito o devido acoplamento entre eles, foram analisados exemplos, que foram comparados com os resultados obtidos por outros pesquisadores, demonstrando sua validade. / For a more accurate analysis of the structural system, it is necessary to study the interactive behavior between the various parts that compose it, among them, there is the interaction between the foundation elements and massive soil. In this work, numerical formulations were developed for the analysis of pile-soil interaction by coupling between different numerical methods: the boundary element method, finite element method and finite difference method. Piles can be subjected to horizontal loads, vertical and moments applied on its top. In these formulations were used in addition to the displacement integral equations, the equations of their derivatives, leading to a higher degree of uniqueness but allowing the adoption of more sophisticated approaches to displacements and contact tractions along the pile. All displacements and their derivatives relating to the pile were matched with the corresponding soil. Developed formulations made due coupling between them were analyzed examples, which were compared with results obtained by other authors, demonstrating its validity.
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