Computation of dendritic microstructures using a level set method

Kim, Yung Tae; Goldenfeld, Nigel; Dantzig, Jonathan A.

doi:10.1103/physreve.62.2471

Cited by 150 publications

(115 citation statements)

References 26 publications

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“…It is important to emphasize that the interface is spatially diffuse and all interpolation functions are smooth in the present phase-field model. Hence, this model remains simple to implement numerically in comparison to other methods that combine sharp and diffuse interface ingredients [30,31].…”

Section: Discussionmentioning

confidence: 99%

Quantitative phase-field model of alloy solidification

et al. 2004

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We present a detailed derivation and thin interface analysis of a phase-field model that can accurately simulate microstructural pattern formation for low-speed directional solidification of a dilute binary alloy. This advance with respect to previous phase-field models is achieved by the addition of a phenomenological "antitrapping" solute current in the mass conservation relation [A. Karma, Phys. Rev. Lett 87, 115701 (2001)]. This antitrapping current counterbalances the physical, albeit artificially large, solute trapping effect generated when a mesoscopic interface thickness is used to simulate the interface evolution on experimental length and time scales. Furthermore, it provides additional freedom in the model to suppress other spurious effects that scale with this thickness when the diffusivity is unequal in solid and liquid [ R. F. Almgren, SIAM J. Appl. Math 59, 2086 (1999)], which include surface diffusion and a curvature correction to the Stefan condition. This freedom can also be exploited to make the kinetic undercooling of the interface arbitrarily small even for mesoscopic values of both the interface thickness and the phase-field relaxation time, as for the solidification of pure melts [A. Karma and W.-J. Rappel, Phys. Rev. E 53, R3017 (1996)].The performance of the model is demonstrated by calculating accurately for the first time within a phase-field approach the Mullins-Sekerka stability spectrum of a planar interface and nonlinear cellular shapes for realistic alloy parameters and growth conditions. 2

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Section: Discussionmentioning

confidence: 99%

Quantitative phase-field model of alloy solidification

et al. 2004

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“…In [29], Chen et al had earlier proposed a similar methodology, except that the treatment of the boundary conditions was different. Kim et al applied that framework to the simulation of the solidification processes in [70]. We note that the first level-set approach to solve the Stefan problem was given in Sethian and Strain [126].…”

Section: A Level-set Approach To the Stefan Problemmentioning

confidence: 99%

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

2012

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We present a review of some of the state-of-the-art numerical methods for solving the Stefan problem and the Poisson and the diffusion equations on irregular domains using (i) the level-set method for representing the (possibly moving) irregular domain's boundary, (ii) the ghost-fluid method for imposing the Dirichlet boundary condition at the irregular domain's boundary and (iii) a quadtree/octree nodebased adaptive mesh refinement for capturing small length scales while significantly reducing the memory and CPU footprint. In addition, we highlight common misconceptions and describe how to properly implement these methods. Numerical experiments illustrate quantitative and qualitative results.

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“…In addition, a Gibbs-Thomson condition relating the temperature of the interface to its local curvature and velocity may also be applied. The level set method has been applied to the dendrite growth problem by a number of authors [32,33] and the technique is potentially very exiting as it removes the problems associated with the diffuse interface used in phase-field methods. However, it is fair to say that the application of the technique is far less well developed than phase-field, with models generally being restricted to single phase, thermally controlled solidification.…”

Section: Discusionmentioning

confidence: 99%

Quantification of mesh induced anisotropy effects in the phase-field method

Mullis

2006

Computational Materials Science

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Phase-field modelling is one of the most powerful techniques currently available for the simulation from first principles the time dependant evolution of complex solidification microstructures. However, unless care is taken the computational mesh used to solve the set of partial differential equations that result from the phase-field formulation of the solidification problem may introduce a stray, or implicit, anisotropy, which would be highly undesirable in quantitative calculations. In this paper we quantify this effect as a function of various computational parameters and subsequently suggest techniques for mitigating the effect of this stray anisotropy. 81.30.Fb, PACS:

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Computation of dendritic microstructures using a level set method

Cited by 150 publications

References 26 publications

Quantitative phase-field model of alloy solidification

Quantitative phase-field model of alloy solidification

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

Quantification of mesh induced anisotropy effects in the phase-field method

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