Adaptive finite elements with high aspect ratio for the computation of coalescence using a phase-field model

Burman, Erik; Jacot, Arthur Paul; Picasso, Marco

doi:10.1016/j.jcp.2003.09.021

Cited by 22 publications

(13 citation statements)

References 27 publications

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“…We therefore solve these equations on an adaptive finite element grid. [21][22][23][24][25][26] The phase field in the interfacial region is always solved on the finest grid. The grid density outside this interfacial region is determined using a hybrid scheme based on a local error estimator and rules that ensure smooth grading of the mesh.…”

Section: Phase-field Modelmentioning

confidence: 99%

Dendritic Growth Morphologies in Al-Zn Alloys—Part II: Phase-Field Computations

Dantzig

Napoli

Friedli

et al. 2013

Metall Mater Trans A

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In Part I of this article, the role of the Zn content in the development of solidification microstructures in Al-Zn alloys was investigated experimentally using X-ray tomographic microscopy. The transition region between h100i dendrites found at low Zn content and h110i dendrites found at high Zn content was characterized by textured seaweed-type structures. This Dendrite Orientation Transition (DOT) was explained by the effect of the Zn content on the weak anisotropy of the solid-liquid interfacial energy of Al. In order to further support this interpretation and to elucidate the growth mechanisms of the complex structures that form in the DOT region, a detailed phase-field study exploring anisotropy parameters' space is presented in this paper. For equiaxed growth, our results essentially recapitulate those of Haxhimali et al. [1] in simulations for pure materials. We find distinct regions of the parameter space associated with h100i and h110i dendrites, separated by a region where hyperbranched dendrites are observed. In simulations of directional solidification, we find similar behavior at the extrema, but in this case, the anisotropy parameters corresponding to the hyperbranched region produce textured seaweeds. As noted in the experimental work reported in Part I, these structures are actually dendrites that prefer to grow misaligned with respect to the thermal gradient direction. We also show that in this region, the dendrites grow with a blunted tip that oscillates and splits, resulting in an oriented trunk that continuously emits side branches in other directions. We conclude by making a correlation between the alloy composition and surface energy anisotropy parameters.

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Section: Phase-field Modelmentioning

confidence: 99%

Dendritic Growth Morphologies in Al-Zn Alloys—Part II: Phase-Field Computations

Dantzig

Napoli

Friedli

et al. 2013

Metall Mater Trans A

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“…Phase-field simulations of particle coalescence utilising a refined finite element mesh without a strong directional structure have been conducted by Burman et al [22]. Although they do not explicitly check whether there is any mesh induced anisotropy, their results on the growth and subsequent coalescence of initially spherical particles would suggest that mesh induced effects in their computational scheme are very small.…”

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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“…The essential idea behind the time evolution phase-field approach is to use the non-zero quantities as source terms in a timedependent relaxation to a steady state satisfying (13). In particular, for the phase and orientation variables, we postulate the Allen-Cahn equations [3] …”

Section: The Phase Field Modelmentioning

confidence: 99%

“…Since PFM diffusion terms result in a time step limit proportional to the inverse square of the mesh size, and a fine mesh may be required to resolve thin interfaces, fully explicit approaches can easily require a prohibitively large number of time steps. For this reason, semi-explicit [11] and fully implicit [12][13][14] integration algorithms have also been investigated. In [14] it is reported that a second-order implicit time discretization scheme with variable time step size control is considerably faster than an Euler explicit scheme for a 2D binary alloy solidification problem.…”

Section: Introductionmentioning

confidence: 99%

A numerical algorithm for the solution of a phase-field model of polycrystalline materials

Dorr

Fattebert

Wickett

et al. 2010

Journal of Computational Physics

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We describe an algorithm for the numerical solution of a phase-field model (PFM) of microstructure evolution in polycrystalline materials. The PFM system of equations includes a local order parameter, a quaternion representation of local orientation and a species composition parameter. The algorithm is based on the implicit integration of a semidiscretization of the PFM system using a backward difference formula (BDF) temporal discretization combined with a Newton-Krylov algorithm to solve the nonlinear system at each time step. The BDF algorithm is combined with a coordinate projection method to maintain quaternion unit length, which is related to an important solution invariant. A key element of the Newton-Krylov algorithm is the selection of a preconditioner to accelerate the convergence of the Generalized Minimum Residual algorithm used to solve the Jacobian linear system in each Newton step. Results are presented for the application of the algorithm to 2D and 3D examples.Key words: Phase-field model, polycrystalline microstructure, method of lines, Newton-Krylov methods 1991 MSC: 35Q99, 65F10, 65H10, 65M06, 65M12, 65M20, 65Z05 * Corresponding author.Email addresses: dorr1@llnl.gov (M. R. Dorr ), fattebert1@llnl.gov (J.-L. Fattebert ), wickett1@llnl.gov (M. E. Wickett ), belak1@llnl.gov (J. F. Belak ), turchi1@llnl.gov (P. E. A. Turchi ).

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Adaptive finite elements with high aspect ratio for the computation of coalescence using a phase-field model

Cited by 22 publications

References 27 publications

Dendritic Growth Morphologies in Al-Zn Alloys—Part II: Phase-Field Computations

Dendritic Growth Morphologies in Al-Zn Alloys—Part II: Phase-Field Computations

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

A numerical algorithm for the solution of a phase-field model of polycrystalline materials

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