An adaptive, fully implicit multigrid phase-field model for the quantitative simulation of non-isothermal binary alloy solidification

Rosam, J.; Jimack, Peter K.; Mullis, Andrew M.

doi:10.1016/j.actamat.2008.05.029

Cited by 64 publications

(73 citation statements)

References 29 publications

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“…The latter we obtain by fitting a parabolic profile to the φ = 0 isoline using a 4 th order interpolation scheme described in [21,34], as this has generally been felt [19,38] to be more directly comparable to analytical dendrite growth theories [5], than the curvature obtained directly from the derivatives of φ at the tip.…”

Section: Description Of the Modelmentioning

confidence: 99%

“…Moreover, in the limited number of cases where phase-field models have been applied to alloy systems solidifying under coupled thermo-solutal control [19,20,21,22], σ * has been found to vary with undercooling, alloy concentration and Lewis number (= ratio of thermal to solutal diffusivity, α/D), with this variation in some cases being non-monotonic. The variation of σ * with concentration appear to be borne out experimentally, with a re-evaluation by Li & Beckermann [23] of the data of Chopra et al [ 24 ] for the transparent succinonitrile-acetone system showing a variation in σ * with concentration of between a factor of 2 and 4 depending upon the undercooling considered.…”

Section: Introductionmentioning

confidence: 99%

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Prediction of the operating point of dendrites growing under coupled thermosolutal control at high growth velocity

Mullis

2011

Phys. Rev. E

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We use a phase-field model for the growth of dendrites in dilute binary alloys under coupled thermo-solutal control to explore the dependence of the dendrite tip velocity and radius of curvature upon undercooling, Lewis number (ratio of thermal to solutal diffusivity), alloy concentration and equilibrium partition coefficient. Constructed in the quantitatively valid thin-interface limit the model uses advanced numerical techniques such as mesh adaptivity, multigrid and implicit time-stepping to solve the non-isothermal alloy solidification problem for materials parameters that are realistic for metals. From the velocity and curvature data we estimate the dendrite operating point parameter, σ*. We find that σ* is non-constant and, over a wide parameter space, displays first a local minimum followed by a local maximum as the undercooling is increased. This behaviour is contrasted with a similar type of behaviour to that predicted by simple marginal stability models to occur in the radius of curvature, on the assumption of constant σ*.

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Section: Description Of the Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Prediction of the operating point of dendrites growing under coupled thermosolutal control at high growth velocity

Mullis

2011

Phys. Rev. E

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“…Quantitative phase-field models are being increasingly utilized for quantitative simulations of solidification phenomena. 34,36,[68][69][70][71][72][73][74][75][76][77][78][79][80][81] As mentioned above, significant progress has been made in quantitative phase-field modeling for alloy solidification. The accuracy of quantitative phase-field simulations is evaluated by observing the convergence behavior of the simulation results with decreasing W. It has been demonstrated that the convergence of the results in quantitative phase-field simulations is much faster than that of the results in the conventional phase-field model, [31][32][33] which indicates that accurate results can be obtained using a large value for W in quantitative phase-field models.…”

Section: Advances In Quantitative Computation Of Solidification Micromentioning

confidence: 99%

Solidification in a Supercomputer: From Crystal Nuclei to Dendrite Assemblages

Shibuta

Ohno

Takaki

2015

JOM

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Thanks to the recent progress in high-performance computational environments, the range of applications of computational metallurgy is expanding rapidly. In this paper, cutting-edge simulations of solidification from atomic to microstructural levels performed on a graphics processing unit (GPU) architecture are introduced with a brief introduction to advances in computational studies on solidification. In particular, million-atom molecular dynamics simulations captured the spontaneous evolution of anisotropy in a solid nucleus in an undercooled melt and homogeneous nucleation without any inducing factor, which is followed by grain growth. At the microstructural level, the quantitative phase-field model has been gaining importance as a powerful tool for predicting solidification microstructures. In this paper, the convergence behavior of simulation results obtained with this model is discussed, in detail. Such convergence ensures the reliability of results of phase-field simulations. Using the quantitative phase-field model, the competitive growth of dendrite assemblages during the directional solidification of a binary alloy bicrystal at the millimeter scale is examined by performing two-and threedimensional large-scale simulations by multi-GPU computation on the supercomputer, TSUBAME2.5. This cutting-edge approach using a GPU supercomputer is opening a new phase in computational metallurgy.

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“…For smoothing the error we use a fully-coupled nonlinear weighted Gauss-Seidel iteration where the number of pre-and post-smoothing operations required for optimal convergence is determined empirically. Full details of the numerical scheme are given in [13,14].…”

Section: Description Of the Modelmentioning

confidence: 99%

“…The governing equations are descretized using a finite difference approximation based upon a quadrilateral, non-uniform, locally-refined mesh with equal grid spacing in both directions [13,14]. This allows the application of standard second order central difference stencils for the calculation of first and second differentials, while a compact 9-point scheme has been used for Laplacian terms, in order to reduce the mesh induced [15] anisotropy.…”

Section: Description Of the Modelmentioning

confidence: 99%

A Phase-Field Model for the Diffusive Melting of Isolated Dendritic Fragments

Mullis

2014

Metall Mater Trans A

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A thermal phase-field model constructed in the 'thin-interface' limit and incorporating a number of advanced numerical techniques as such adaptive mesh refinement, implicit time-stepping and a multigrid solver has been used to study the isolated diffusive melting of dendritic fragments. The results of the simulations are found to be fully consistent with the experimental observation of such melting in microgravity during the Isothermal Dendrite Growth Experiment. It is found that the rate at which the ratio of semi-major to semi-minor axes changes is a function of the melt Stefan number, which may help explain why both melting at (approximately) constant ratio and melting at slowly increasing ratio have been observed.

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An adaptive, fully implicit multigrid phase-field model for the quantitative simulation of non-isothermal binary alloy solidification

Cited by 64 publications

References 29 publications

Prediction of the operating point of dendrites growing under coupled thermosolutal control at high growth velocity

Prediction of the operating point of dendrites growing under coupled thermosolutal control at high growth velocity

Solidification in a Supercomputer: From Crystal Nuclei to Dendrite Assemblages

A Phase-Field Model for the Diffusive Melting of Isolated Dendritic Fragments

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