Design and Verification of the MPFA Scheme for Three-Dimensional Phase Field Model of Dendritic Crystal Growth

Strachota, Pavel; Beneš, Michal

doi:10.1007/978-3-642-33134-3_49

Cited by 4 publications

(17 citation statements)

References 19 publications

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“…The latent heat release is focused at the interface where the gradient is nonzero. Several computational studies have been performed using this model, both in 2D [30,41,29,42]and in 3D [32,33,34]. However, for a very large supercooling, this model seems to be failing as well (see Section 5.5).…”

Section: The Kobayashi Modelmentioning

confidence: 99%

“…In this paper, we investigate a family of phase field models for simulating dendritic growth of a pure supercooled substance designed in our previous work [29] and related to [7]. These models were used in qualitative computational studies in both 2D [29,30,31] and 3D [32] and efficient parallel numerical solvers were implemented by means of the finite volume method [33]. Extensions to polycrystalline solidification were also implemented [34,35].…”

Section: Introductionmentioning

confidence: 99%

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Focusing the Latent Heat Release in 3D Phase Field Simulations of Dendritic Crystal Growth

Strachota,

Wodecki,

Beneš

2020

Preprint

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We investigate a family of phase field models for simulating dendritic growth of a pure supercooled substance. Our aim is to remove limitations inherent to some existing models both in terms of the applicability to physically realistic situations and the feasibility of mathematical and numerical analysis. The central object of interest is the reaction term in the Allen-Cahn equation, which is responsible for spatial distribution of latent heat release during solidification. Several existing forms of the reaction term are analyzed and new variants are proposed, with consistent asymptotic behavior as the interface thickness tends to zero. The resulting models are tested in a number of numerical simulations focusing on mesh-dependence, model parameter settings, and the applicability to solidification under very large supercooling.

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Section: The Kobayashi Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Focusing the Latent Heat Release in 3D Phase Field Simulations of Dendritic Crystal Growth

Strachota,

Wodecki,

Beneš

2020

Preprint

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“…The numerical scheme for solving (1)-(5) with the original setting (7) has already been described in [4]. Its efficient MPI/OpenMP hybrid parallel implementation [5] has been the basis for further modifications introduced in this paper.…”

Section: Numerical Algorithmsmentioning

confidence: 99%

“…Effect of the numerical mesh simulations with common parameters listed in Fig. 5 and a single crystallization seed centered at (4,4,4). Slice through the crystal surface by the plane z = 4.…”

Section: Parallel Implementation Of the Oif Update Algorithmmentioning

confidence: 99%

“…The model in question [1] describes single component melt solidification with anisotropic surface tension [2,3]. We elaborate on our existing numerical algorithm [4] and its parallel implementation [5] in order to simulate the growth of multiple crystals with random orientations. Unlike the works [6,7] based on the multi-phase-field method, our approach involves a single phase field together with orientation information handled separately.…”

Section: Introductionmentioning

confidence: 99%

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High Resolution 3D Phase Field Simulations of Single Crystal and Polycrystalline Solidification

Strachota

Wodecki

2018

Acta Phys. Pol. A

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We deal with numerical solution of a three-dimensional phase field model of solidification in single component anisotropic materials. In this contribution, we extend the model by crystal orientation transformation. A robust algorithm is then developed to simulate the growth of multiple grains with an arbitrary number of random crystallographic orientations and a fully resolved 3D dendritic geometry. In the first part, the model and the parallel implementation of the algorithms are explained. The second part is devoted to demonstrating the effect of meshrelated numerical anisotropy and the simulations of complex polycrystalline solidification on very fine meshes.

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Error estimate of the finite volume scheme for the Allen–Cahn equation

Strachota

Beneš

2017

Bit Numer Math

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Design and Verification of the MPFA Scheme for Three-Dimensional Phase Field Model of Dendritic Crystal Growth

Cited by 4 publications

References 19 publications

Focusing the Latent Heat Release in 3D Phase Field Simulations of Dendritic Crystal Growth

Focusing the Latent Heat Release in 3D Phase Field Simulations of Dendritic Crystal Growth

High Resolution 3D Phase Field Simulations of Single Crystal and Polycrystalline Solidification

Error estimate of the finite volume scheme for the Allen–Cahn equation

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