A phase-field model with convection

numerical simulations
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U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology , [Gaithersburg, MD]
Dendritic crystals -- Mathematical models., Crystal growth -- Mathematical models., Heat -- Convection -- Mathematical mo
Other titlesPhase field model with convection.
StatementD.M. Anderson, G.B. McFadden, A.A. Wheeler.
SeriesNISTIR -- 6442.
ContributionsMcFadden, Geoffrey B., Wheeler, A. A., National Institute of Standards and Technology (U.S.)
The Physical Object
FormatMicroform
Pagination15 p.
ID Numbers
Open LibraryOL17716845M

We develop a phase-field model for the solidification of a pure material that includes convection in the liquid phase. The model permits the interface to have an anisotropic surface energy, and allows a quasi-incompressible thermodynamic description in which the densities Cited by: A phase-field model is a mathematical model for solving interfacial problems.

It has mainly been applied to solidification dynamics, but it has also been applied to other situations such as viscous fingering, fracture mechanics, hydrogen embrittlement, and vesicle dynamics. The method substitutes boundary conditions at the interface by a partial differential equation for the evolution of an.

Abstract In a previously developed phase-field model of solidification that includes convection in the melt, the two phases are represented as viscous liquids, where the putative solid phase has a viscosity much larger than the liquid by: 4.

A phase-field model for the solidification of a pure material that incorporates convection has recently been developed. This model is a two-fluid model in which the solid phase is modeled as a sufficiently viscous by: 1.

We have previously developed a phase-field model of solidification that includes convection in the melt [Physica D () ]. This model represents the two phases as viscous liquids, where. We have previously developed a phase-field model of solidification that includes convection in the melt [Physica D () ].

This model represents the two phases as viscous liquids, where the putative solid phase has a viscosity much larger than the liquid by: PHASE-FIELD MODEL WITH CONVECTION FIG. Schematic illustration of the diffuse solid–liquid interface, the averaging volume, and the phase-field variable variation normal to the interface.

equations are needed that are valid not only in the solid and liquid phases, but also in the diffuse interface region. Get this from a library. A phase-field model with convection: numerical simulations.

[D M Anderson; Geoffrey B McFadden; A A Wheeler; National Institute of Standards and Technology (U.S.)]. A number of formulations of the phase A phase-field model with convection book model are based on a free energy function depending on an order parameter (the phase field) and a diffusive field (variational formulations).

Equations of the model are then obtained by using general relations of statistical a function is constructed from physical considerations, but contains a parameter or combination of parameters. Recently we proposed a phase field model to describe Marangoni convection in a compressible fluid of van der Waals type far from criticality [Eur.

Phys. B 44, ()]. Get this from a library. A phase-field model with convection: sharp-interface asymptotics. [D M Anderson; Geoffrey B McFadden; A A Wheeler; National Institute of Standards and Technology (U.S.)]. The phase field crystal (PFC) model essentially resolves systems on atomic length and diffusive timescales and as such lies somewhere in between standard phase field modeling and atomic methods.

This chapter reviews the PFC model, which is just a conserved version of a model developed for Rayleigh‐Benard convection, known as the Swift. Phase-Field Models Mathis Plapp Physique de la Mati`ere Condens´ee, Ecole Polytechnique, CNRS,´ Palaiseau, France Abstract.

Phase-field models have become popular in recent years to describe a host of free-boundary problems in various areas of re-search. The key point of the phase-field approach is that surfacesFile Size: KB.

() Efficient numerical scheme for a dendritic solidification phase field model with melt convection. Journal of Computational Physics() A Crank–Nicolson discontinuous finite volume element method for a coupled non-stationary Stokes–Darcy by: Abstract.

Phase-field models have become popular in recent years to describe a host of free-boundary problems in various areas of research. The key point of the phase-field approach is that surfaces and interfaces are implicitly described by continuous scalar fields that take constant values in the bulk phases and vary continuously but steeply across a diffuse by: We consider a tridimensional phase-field model for a solidification/melting non-stationary process, which incorporates the physics of binary alloys, thermal properties and fluid motion of non-solidified material.

The model is a free-boundary value problem consisting of a highly non-linear parabolic system including a phase-field equation, a heat equation, a concentration equation and a variant Cited by: We develop a phase-field model for the solidification of a pure material that includes convection in the liquid phase.

The model permits the interface to have an anisotropic surface energy, and allows a quasi-incompressible thermodynamic description in which the densities in the solid and liquid phases may each be uniform.

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The solid phase is modeled as an extremely viscous liquid, and the Cited by: () Continuous finite element schemes for a phase field model in two-layer fluid Bénard–Marangoni convection computations. Computer Physics Communications() An adaptive meshfree method for phase-field models of by: Book Chapters.

Bures, A. Moure, H. Gomez, Computational treatment of interface dynamics via phase-field modeling, Numerical Simulation in Physics and Engineering: Trends and Applications, Springer, H. Gomez, J. Bueno, Interaction of multiphase fluids and solid structures, Frontiers in Computational Fluid-Structure Interaction and Flow Simulation.

A phase-field model with convection D. Anderson Not In Library. Principles of solidification Bruce Chalmers Not In Library. A phase-field model of solidification with convection D. Anderson Not In Library. A phase-field model with convection1 book Conference on Modeling of Casting and Welding Processes (3rd Santa Barbara.

Physica D () – A phase-field model with convection: sharp-interface asymptotics D.M.

Description A phase-field model with convection EPUB

Andersona,∗, G.B. McFaddenb, A.A. Wheelerc a Department of Mathematical Sciences, George Mason University, Fairfax, VAUSA b Mathematical and Computational Sciences Division, National Institute of Standards and Technology, Gaithersburg, MDUSA. Planas and J.L.

Boldrini, A bidimensional phase-field model with convection for change phase of an alloy, J. Math. Anal.

Details A phase-field model with convection PDF

Appl. (), – CrossRef MathSciNet zbMATH Google Scholar [11] J.F. Rodrigues, Variational methods in the Stefan problem, pp– in Phase Transitions and Hysteresis, Lecture Notes Math., Vol.

Author: Takesi Fukao. Kim S G A phase-field model with antitrapping current for multicomponent alloys with Diepers H-J, Steinbach I, Karma A and Tong X Modeling melt convection in phase-field simulations of solidification J.

Comput ) (The Metals Society Book ) (London: Metals Society) pp Google Scholar. Kurz W and Fisher D J Cited by: In this paper we derive thermodynamically consistent higher order phase field models for the dynamics of biomembranes in incompressible viscous fluids.

We start with basic conservation laws and an appropriate version of the second law of thermodynamics and obtain generalizations of models introduced by Du, Li and Liu [3] and Jamet and Misbah [11].Cited by: 6.

Phase field method R. Qin1 and H. Bhadeshia*2 In an ideal scenario, a phase field model is able to compute quantitative aspects of the evolution of microstructure without explicit intervention. The method is particularly appealing because it provides a visual impression of the development of structure, one which often matches observations.

PHASE-FIELD SIMULATIONS OF Nd-Fe-B: NUCLEATION AND GROWTH KINETICS DURING PERITECTIC GROWTH Introduction Phase-Field Model with Hydrodynamic Convection Investigating Heterogeneous Nucleation in Peritectic Materials via the Phase-Field Method Conclusion INVESTIGATIONS OF PHASE SELECTION IN UNDERCOOLED MELTS OF Nd-Fe-B ALLOYS.

The simulation was performed using the phase-field model published in: J.C. Ramirez, C. Beckermann, A. Karma, and H.J. Diepers, "Phase-field modeling of binary alloy solidification with coupled heat and solute diffusion," Physical Review E, Vol.

69, (16 pages),   The model aims to describe in a thermodynamically consistent way the phase change phenomenon coupled with the macroscopic motion of the fluid. The phase field φ ∈ [0, 1] describes the liquid fraction at any point and the overall water density is a function of the phase field and the pressure.

An extra gaseous substance (e.g. air) is allowed Cited by: 2. Development of a Phase-Field Model for Simulating Dendritic Growth in a Convection-Dominated Flow Field C. Chen and Tony W. Sheu 23 October | Numerical Heat Transfer, Part B: Fundamentals, Vol.

66, No. The simplest phase field model can be written as a system of parabolic equations for temperature T (t,x) and phase or “order” parameter A (t,z) so that A near 0 is one phase, e.g., solid, while A near 1 is the other, e.g., liquid.

An order parameter for a particular. The next step towards application of phase-field models in materials science was the alloy solidification model by Wheeler, Boettinger and McFadden in They combined the Cahn–Hilliard model for spinodal decomposition and early phase-field models by Langer [ 13 ], Collins and Levine [ 26 ], Caginalp [ 27 ] and Kobayashi [ 22 ].Cited by: A phase field model for vesicle-substrate adhesion, with J.

Zhang and S. Das, J. Computational Phys., An explicit-implicit predictor-corrector domain decomposition method for time dependent multi-dimensional convection diffusion equations, with L.

Zhu and G. Yuan, Numerical Mathematics: Theory, Methods and Applications.Jeong, Jun-Ho Goldenfeld, Nigel and Dantzig, Jonathan A. Phase field model for three-dimensional dendritic growth with fluid al Review E, Vol. 64, Issue. 4,Cited by: