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Three-dimensional, fully adaptive simulations of phase-field fluid models

CENICEROS, Hector D.; NOS, Rudimar L.; ROMA, Alexandre M.
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
66.69298%
We present an efficient numerical methodology for the 31) computation of incompressible multi-phase flows described by conservative phase-field models We focus here on the case of density matched fluids with different viscosity (Model H) The numerical method employs adaptive mesh refinements (AMR) in concert with an efficient semi-implicit time discretization strategy and a linear, multi-level multigrid to relax high order stability constraints and to capture the flow`s disparate scales at optimal cost. Only five linear solvers are needed per time-step. Moreover, all the adaptive methodology is constructed from scratch to allow a systematic investigation of the key aspects of AMR in a conservative, phase-field setting. We validate the method and demonstrate its capabilities and efficacy with important examples of drop deformation, Kelvin-Helmholtz instability, and flow-induced drop coalescence (C) 2010 Elsevier Inc. All rights reserved; NSF; NSF[DMS 0609996]; FAPESP[04/13781-1]; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); FAPESP[06/57099-5]; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); CNPq[307348/2008-3]; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

"Simulações de escoamentos tridimensionais bifásicos empregando métodos adaptativos e modelos de campo fase"; "Simulations of 3D two-phase flows using adaptive methods and phase field models"

Nós, Rudimar Luiz
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Relevância na Pesquisa
66.811387%
Este é o primeiro trabalho que apresenta simulações tridimensionais completamente adaptativas de um modelo de campo de fase para um fluido incompressível com densidade de massa constante e viscosidade variável, conhecido como Modelo H. Solucionando numericamente as equações desse modelo em malhas refinadas localmente com a técnica AMR, simulamos computacionalmente escoamentos bifásicos tridimensionais. Os modelos de campo de fase oferecem uma aproximação física sistemática para investigar fenômenos que envolvem sistemas multifásicos complexos, tais como fluidos com camadas de mistura, a separação de fases sob forças de cisalhamento e a evolução de micro-estruturas durante processos de solidificação. Como as interfaces são substituídas por delgadas regiões de transição (interfaces difusivas), as simulações de campo de fase requerem muita resolução nessas regiões para capturar corretamente a física do problema em estudo. Porém essa não é uma tarefa fácil de ser executada numericamente. As equações que caracterizam o modelo de campo de fase contêm derivadas de ordem elevada e intrincados termos não lineares...

Numerical simulation of solute trapping phenomena using phase-field solidification model for dilute binary alloys

Fonte: ABM, ABC, ABPol Publicador: ABM, ABC, ABPol
Tipo: Artigo de Revista Científica Formato: text/html
Relevância na Pesquisa
66.663135%
Numerical simulation of solute trapping during solidification, using two phase-field model for dilute binary alloys developed by Kim et al. [Phys. Rev. E, 60, 7186 (1999)] and Ramirez et al. [Phys. Rev. E, 69, 05167 (2004)] is presented here. The simulations on dilute Cu-Ni alloy are in good agreement with one dimensional analytic solution of sharp interface model. Simulation conducted under small solidification velocity using solid-liquid interface thickness (2λ) of 8 nanometers reproduced the solute (Cu) equilibrium partition coefficient. The spurious numerical solute trapping in solid phase, due to the interface thickness was negligible. A parameter used in analytical solute trapping model was determined by isothermal phase-field simulation of Ni-Cu alloy. Its application to Si-As and Si-Bi alloys reproduced results that agree reasonably well with experimental data. A comparison between the three models of solute trapping (Aziz, Sobolev and Galenko [Phys. Rev. E, 76, 031606 (2007)]) was performed. It resulted in large differences in predicting the solidification velocity for partition-less solidification, indicating the necessity for new and more acute experimental data.

The effect of adding boron in solidification microstructure of dilute iron-carbon alloy as assessed by phase-field modeling

Fonte: ABM, ABC, ABPol Publicador: ABM, ABC, ABPol
Tipo: Artigo de Revista Científica Formato: text/html
Relevância na Pesquisa
66.505967%
Alloying element like boron, even in small addition, is well known to improve hardenability of steels. Its application can improve mechanical properties of steels and reduce alloying costs. Despite these benefits is not easy to cast boron steels, mainly in dynamical solidification process like continuous casting, due to their crack susceptibility1,2. The strategy of using Phase-Field simulation of the solidification process is based on its proved capacity of predicting realistic microstructure that emerge during solidification under conditions even far from equilibrium3-5. Base on this, some comparative simulations were performed using a three component dilute alloy in a two dimensional domain under unconstrained (isothermal) and constrained (directional) solidification. Simulation results suggested two fragile mechanisms: one related to a deep dendritic primary arms space and other due to the remelting of this region at low temperature. Both resulted mainly from the high boron segregation in interdendritic regions.

Microsegregation in Fe-C-P ternary alloys using a phase-field model

Fonte: Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM Publicador: Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM
Tipo: Artigo de Revista Científica Formato: text/html
Relevância na Pesquisa
66.505967%
A phase-field model is proposed for the simulation of microstructure and solute concentration during the solidification process of Fe-C-P ternary alloys. A relation between material properties and model parameters is presented. Two-dimensional computation results exhibit dendrites in Fe-C-P alloys for different phosphorus concentrations. Alterations in the phosphorus concentration appear to affect the advance speed of the solid-liquid interface. Such an alteration is due to the small diffusivity of phosphorus during the solidification process.

Numerical simulation of the solidification of pure melt by a phase-field model using an adaptive computation domain

Ferreira,Alexandre Furtado; Ferreira,Leonardo de Olivé; Assis,Abner da Costa
Fonte: Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM Publicador: Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM
Tipo: Artigo de Revista Científica Formato: text/html
Relevância na Pesquisa
66.505967%
In this paper, we present a phase-field model with a grid based on the Finite-Difference Method, for improvement of computational efficiency and reducing the memory size requirement. The numerical technique, which is based on the temperature change of the pure material, enables us to use, in the initial steps of the computation, a very small computational domain. Subsequently, in the course of the simulation of the solidification process, the computation domain expands around the dendrite. The computation showed that the dendrite with well-developed secondary arms can be obtained with low computation time and moderate memory demand. The computational efficiency of this numerical technique, the microstructural evolution during the solidification, and competitive growth between side-branches are discussed.

Grain Growth in Thin Films with a Fibre Texture Studied by Phase-Field Simulations and Mean Field Modelling

Moelans, N.; Spaepen, Frans A.; Wollants, P.
Fonte: Taylor & Francis Publicador: Taylor & Francis
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
66.624795%
The evolution of fiber textured structures is simulated in 2 dimensions using a generalized phase field model assuming two forms for the misorientation, a steady-state regime is reached after a finite amount of grain growth, where the numer and length weighted misorientation distribution functions (MDF) are constant in time, and the mean grain area A as a function of time t follows a power growth law A - A0 = kt^n with n close to 1 and A0 the initial mean grain area. The final shape of the MDF and value of the prefactor k in the power growth law clearly correlate with the misorientation dependence of the grain boundary energy. From a quantitative point of view, the fraction of special boundaries obtained in simulations is quite sensitive to the number of possible discrete orientations. Furthermore, a mean field approach is worked out to predict the growth exponent for systems with nonuniform grain boundary energy. The conclusions from the mean field approach are consistent with the simulation results.; Physics

Phase field model for precipitates in crystals

She, Minggang
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 270 p.
Português
Relevância na Pesquisa
46.900977%
Oxygen precipitate caused by oxygen supersaturation is the most common and important defects in Czochralski (CZ) silicon. The presence of oxygen precipitate in silicon wafer has both harmful and beneficial effects on the microelectronic device production. Oxygen precipitates are useful for gathering metallic contaminants away from the device regions and for increasing the mechanical strength of the wafer [Borghesi, 1995], but they also can destroy the electrical and mechanical characteristics of the semiconductor and microelectronic devices [Abe, 1985; Kolbesen, 1985]. The understanding of the mechanism of the formation and growth of the oxygen precipitates in CZ silicon is a key to improve the quality of silicon wafer. The goal of this thesis is to provide a full understanding of the growth of an isolated oxygen precipitate in CZ silicon and its morphological evolution by means of phase-field method, and to gain the insight of the morphological transition of the oxygen precipitate and the distribution of oxygen, vacancy, and self-interstitial around the single oxygen precipitate. The traditional approach to simulate multiphase system is the sharp interface model. Sharp interface model requires tracking the interface between phases...

Viscous Fingering In Complex Magnetic Fluids: Weakly Nonlinear Analysis, Stationary Solutions And Phase-field Models

Lira, Sérgio Henrique Albuquerque; Miranda Neto, José Américo de (Orientador)
Português
Relevância na Pesquisa
66.505967%

The effect of adding boron in solidification microstructure of dilute iron-carbon alloy as assessed by phase-field modeling

Furtado, Henrique Silva; Bernardes, Am?rico Trist?o; Machado, Romuel Figueiredo; Silva, Carlos Ant?nio da
Português
Relevância na Pesquisa
66.505967%
Alloying element like boron, even in small addition, is well known to improve hardenability of steels. Its application can improve mechanical properties of steels and reduce alloying costs. Despite these benefits is not easy to cast boron steels, mainly in dynamical solidification process like continuous casting, due to their crack susceptibility 1,2 . The strategy of using Phase-Field simulation of the solidification process is based on its proved capacity of predicting realistic microstructure that emerge during solidification under conditions even far from equilibrium 3-5 . Base on this, some comparative simulations were performed using a three component dilute alloy in a two dimensional domain under unconstrained (isothermal) and constrained (directional) solidification. Simulation results suggested two fragile mechanisms: one related to a deep dendritic primary arms space and other due to the remelting of this region at low temperature. Both resulted mainly from the high boron segregation in interdendritic regions.

Numerical simulation of solute trapping phenomena using phase-field solidification model for dilute binary alloys

Furtado, Henrique Silva; Bernardes, Am?rico Trist?o; Machado, Romuel Figueiredo; Silva, Carlos Ant?nio da
Português
Relevância na Pesquisa
66.73013%
Numerical simulation of solute trapping phenomena using phase-field solidification model for dilute binary alloys Numerical simulation of solute trapping during solidification, using two phase-field model for dilute binary alloys developed by Kim et al. [Phys. Rev. E, 60, 7186 (1999)] and Ramirez et al. [Phys. Rev. E, 69, 05167 (2004)] is presented here. The simulations on dilute Cu-Ni alloy are in good agreement with one dimensional analytic solution of sharp interface model. Simulation conducted under small solidification velocity using solid liquid interface thickness (2?) of 8 nanometers reproduced the solute (Cu) equilibrium partition coefficient. The spurious numerical solute trapping in solid phase, due to the interface thickness was negligible. A parameter used in analytical solute trapping model was determined by isothermal phase-field simulation of Ni-Cu alloy. Its application to Si-As and Si-Bi alloys reproduced results that agree reasonably well with experimental data. A comparison between the three models of solute trapping (Aziz, Sobolev and Galenko [Phys. Rev. E, 76, 031606 (2007)]) was performed. It resulted in large differences in predicting the solidification velocity for partition-less solidification...

Simulation of the solidification of pure nickel via the phase-field method

Fonte: ABM, ABC, ABPol Publicador: ABM, ABC, ABPol
Tipo: Artigo de Revista Científica Formato: text/html
Relevância na Pesquisa
66.663135%
The Phase-Field method was applied to simulate the solidification of pure nickel dendrites and the results compared with those predicted by the solidification theory and with experimental data reported in the literature. The model's behavior was tested with respect to some initial and boundary conditions. For an initial condition without supercooling, the smooth interface of the solid phase nucleated at the edges of the domain grew uniformly into the liquid region, without branching. In an initially supercooled melt, the interface became unstable under 260 K supercooling, generating ramifications into the liquid region. The phase-field results for dendrite tip velocity were close to experimental results reported in the literature for supercooling above 50 K, but they failed to describe correctly the nonlinear behavior predicted by the collision-limited growth theory and confirmed by experimental data for low supercooling levels.

A Dynamic Multiscale Phase-field Model for Structural Transformations and Twinning: Regularized Interfaces with Transparent Prescription of Complex Kinetics and Nucleation

Agrawal, Vaibhav; Dayal, Kaushik
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.817476%
The motion of microstructural interfaces is important in modeling materials that undergo twinning and structural phase transformations. Continuum models fall into two classes: sharp-interface models, where interfaces are singular surfaces; and regularized-interface models, such as phase-field models, where interfaces are smeared out. The former are challenging for numerical solutions because the interfaces need to be explicitly tracked, but have the advantage that the kinetics of existing interfaces and the nucleation of new interfaces can be transparently and precisely prescribed. In contrast, phase-field models do not require explicit tracking of interfaces, thereby enabling relatively simple numerical calculations, but the specification of kinetics and nucleation is both restrictive and extremely opaque. This prevents straightforward calibration of phase-field models to experiment and/or molecular simulations, and breaks the multiscale hierarchy of passing information from atomic to continuum. We present the formulation of a phase-field model -- i.e., a model with regularized interfaces that do not require explicit numerical tracking -- that allows for easy and transparent prescription of complex interface kinetics and nucleation. The key ingredients are a re-parametrization of the energy density to clearly separate nucleation from kinetics; and an evolution law that comes from a conservation statement for interfaces. This enables clear prescription of nucleation through the source term of the conservation law and of kinetics through an interfacial velocity field. A formal limit of the kinetic driving force recovers the classical continuum sharp-interface driving force...

Interface kinetics in phase field models: isothermal transformations in binary alloys and steps dynamics in molecular-beam-epitaxy

Boussinot, G.; Brener, Efim A.
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.870796%
We present a unified description of interface kinetic effects in phase field models for isothermal transformations in binary alloys and steps dynamics in molecular-beam-epitaxy. The phase field equations of motion incorporate a kinetic cross-coupling between the phase field and the concentration field. This cross coupling generalizes the phenomenology of kinetic effects and was omitted until recently in classical phase field models. We derive general expressions (independent of the details of the phase field model) for the kinetic coefficients within the corresponding macroscopic approach using a physically motivated reduction procedure. The latter is equivalent to the so-called thin interface limit but is technically simpler. It involves the calculation of the effective dissipation that can be ascribed to the interface in the phase field model. We discuss in details the possibility of a non positive definite matrix of kinetic coefficients, i.e. a negative effective interface dissipation, although being in the range of stability of the underlying phase field model. Numerically, we study the step-bunching instability in molecular-beam-epitaxy due to the Ehrlich-Schwoebel effect, present in our model due to the cross-coupling. Using the reduction procedure we compare the results of the phase field simulations with the analytical predictions of the macroscopic approach.

A Stochastic Phase-Field Model Computed From Coarse-Grained Molecular Dynamics

von Schwerin, Erik
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.805967%
Results are presented from numerical experiments aiming at the computation of stochastic phase-field models for phase transformations by coarse-graining molecular dynamics. The studied phase transformations occur between a solid crystal and a liquid. Nucleation and growth, sometimes dendritic, of crystal grains in a sub-cooled liquid is determined by diffusion and convection of heat, on the macroscopic level, and by interface effects, where the width of the solid-liquid interface is on an atomic length-scale. Phase-field methods are widely used in the study of the continuum level time evolution of the phase transformations; they introduce an order parameter to distinguish between the phases. The dynamics of the order parameter is modelled by an Allen--Cahn equation and coupled to an energy equation, where the latent heat at the phase transition enters as a source term. Stochastic fluctuations are sometimes added in the coupled system of partial differential equations to introduce nucleation and to get qualitatively correct behaviour of dendritic side-branching. In this report the possibility of computing some of the Allen-Cahn model functions from a microscale model is investigated. The microscopic model description of the material by stochastic...

Thermodynamic consistency and fast dynamics in phase field crystal modeling

Cheng, Mowei; Cottenier, Stefaan; Emmerich, Heike
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.799814%
A general formulation is presented to derive the equation of motion and to demonstrate thermodynamic consistency for several classes of phase field models at once. It applies to models with a conserved phase field, describing either uniform or periodic stable states, and containing slow as well as fast thermodynamic variables. The approach is based on an entropy functional formalism previously developed in the context of phase field models for uniform states [P. Galenko and D. Jou, Phys. Rev. E {\bf 71}, 046125 (2005)] and thus allows to extend several properties of the latter to phase field models for periodic states (phase field crystal models). In particular, it allows to demonstrate the concept of thermodynamic consistency for phase field crystal models with fast dynamics.; Comment: This paper has been withdrawn due to incompleteness

Derivation of the phase field crystal model for colloidal solidification

van Teeffelen, Sven; Backofen, Rainer; Voigt, Axel; Löwen, Hartmut
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.799814%
The phase-field crystal model is by now widely used in order to predict crystal nucleation and growth. For colloidal solidification with completely overdamped individual particle motion, we show that the phase-field crystal dynamics can be derived from the microscopic Smoluchowski equation via dynamical density functional theory. The different underlying approximations are discussed. In particular, a variant of the phase-field crystal model is proposed which involves less approximations than the standard phase-field crystal model. We finally test the validity of these phase-field crystal models against dynamical density functional theory. In particular, the velocities of a linear crystal front from the undercooled melt are compared as a function of the undercooling for a two-dimensional colloidal suspension of parallel dipoles. Good agreement is only obtained by a drastic scaling of the free energies in the phase-field crystal model in order to match the bulk freezing transition point.; Comment: 11 pages, 5 figures; corrected typos, minor changes after review

Phase field equation in the singular limit of the Stefan problem

Koga, Jun-ichi; Koga, Jiro; Homma, Shunji
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.817476%
The classical Stefan problem is reduced as the singular limit of phase-field equations. These equations are for temperature $u$ and the phase-field $\varphi$, consists of a heat equation: $$u_t+\ell\varphi_t=\Delta u,$$ and a Ginzburg-Landau equation: $$\epsilon\varphi_t=\epsilon\Delta\varphi -\frac{1}{\epsilon}W^\prime (\varphi )+\ell (\varphi )u,$$ where $\ell$ is a latent heat and $W$ is a double-well potential whose wells, of equal depth, correspond to the solid and liquid phases. When $\epsilon\to 0$, the velocity of the moving boundary $v$ in one dimension and that of the radius in the cylinder or sphere are shown as the following Stefan problem,\\ $$\left\{ \begin{array}{l} u_t-\Delta u =0\\\\ \displaystyle v=\frac{1}{2}\left[\frac{\partial u}{\partial n}\right]_\Gamma \displaystyle u=-\frac{m}{2\ell}[\kappa -\alpha v]_\Gamma \end{array} \right.$$ where $\alpha$ is a positive parameter, $[\frac{\partial u}{\partial n}]_\Gamma$ is the jump of the normal derivatives of $u$ (from solid to liquid), and $m=\int_{-1}^1\left(2W(\varphi)\right)^{1/2}d\varphi$. Since it is sufficient to describe the phase transition of single component by the phase-field equation, we analyze the phase-field equation, and investigate whether the equation shows the Stefan problem or not. The velocity of the moving boundary in the cylinder and sphere are determined and the result of the simulation of the equation is also presented. Next...

Adaptive Spline-based Finite Element Method with Application to Phase-field Models of Biomembranes

Jiang, Wen
Tipo: Dissertação
Relevância na Pesquisa
66.505967%

Interfaces play a dominant role in governing the response of many biological systems and they pose many challenges to traditional finite element. For sharp-interface model, traditional finite element methods necessitate the finite element mesh to align with surfaces of discontinuities. Diffuse-interface model replaces the sharp interface with continuous variations of an order parameter resulting in significant computational effort. To overcome these difficulties, we focus on developing a computationally efficient spline-based finite element method for interface problems.

A key challenge while employing B-spline basis functions in finite-element methods is the robust imposition of Dirichlet boundary conditions. We begin by examining weak enforcement of such conditions for B-spline basis functions, with application to both second- and fourth-order problems based on Nitsche's approach. The use of spline-based finite elements is further examined along with a Nitsche technique for enforcing constraints on an embedded interface. We show that how the choice of weights and stabilization parameters in the Nitsche consistency terms has a great influence on the accuracy and robustness of the method. In the presence of curved interface...

Modeling Microdomain Evolution on Giant Unilamellar Vesicles using a Phase-Field Approach

Embar, Anand Srinivasan