Reduction of discretisation-induced anisotropy in the phase-field modelling of dendritic growth by meshless approach

Dobravec, Tadej; Mavrič, Boštjan; Šarler, Božidar

doi:10.1016/j.commatsci.2019.109166

Cited by 19 publications

(17 citation statements)

References 40 publications

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“…Phase field models can be sensitive to the discretization (mesh-induced anisotropy). In order to study if these results are influenced by the meshes, we have run simulations of growing crystal of different orientations (Dobravec et al, 2020) It is also interesting to study how the substrate's curvature influences the selection of tip radius and propagation velocity of dendrites. In order to obtain the tip radius, we measured from the simulations the geodesic curvature of the interface at the tips as a function of the size of the spherical substrate.…”

Section: Resultsmentioning

confidence: 99%

Phase Field Modeling of Dendritic Growth on Spherical Surfaces

Ortellado

Gómez

2020

Front. Mater.

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The spontaneous formation of a crystal phase is one of the most common and beautiful pattern formation mechanisms in nature. Different instabilities in the crystal interface may lead to the growth of ramified structures, known as dendritic crystal growth. In this work, we use a Phase Field Model and numerical simulations to study 2D dendritic growth on curved surfaces. We show how the degree of ramification of a growing nucleus is modified by the underlying curvature of the substrate.

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Section: Resultsmentioning

confidence: 99%

Phase Field Modeling of Dendritic Growth on Spherical Surfaces

Ortellado

Gómez

2020

Front. Mater.

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“…We employ fifth-degree polyharmonic splines as radial basis functions, second-order augmentation with monomials, and thirteen nodes in a local support domain in the meshless RBF-FD method. We have previously shown that such a configuration is very suitable out of many tested configurations for the PF modelling of dendritic growth [6,7].…”

Section: Anisotropy Of the Surface Energymentioning

confidence: 99%

“…In the previous studies, we consider PF models for simulating single dendrite growth in pure melts and dilute binary alloys [6,7]. In this paper, we extend the test case for the single dendrite solidification of dilute binary alloys [8] to polycrystalline solidification.…”

Section: Introductionmentioning

confidence: 99%

“…In the present study, we employ the local radial basis function collocation method (LRBFCM) [28], also known as the radial basis function generated finite difference (RBF-FD) method [29]. The meshless RBF-FD method is especially suitable for orientation-insensitive PF modelling of dendritic solidification in arbitrary preferential growth directions [6].…”

Section: Introductionmentioning

confidence: 99%

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Application of a meshless space-time adaptive approach to phase-field modelling of polycrystalline solidification

Dobravec

Mavrič

Šarler

2023

IOP Conf. Ser.: Mater. Sci. Eng.

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We have developed a 2-D numerical meshless adaptive approach for phase-field modelling of dendritic solidification. The quadtree-based approach decomposes the computational domain into quadtree sub-domains of different sizes. The algorithm generates uniformly-distributed computational nodes in each quadtree sub-domain. We apply the meshless radial basis function generated finite difference method and the forward Euler scheme to discretise governing equations in each computational node. The fixed ratio between the characteristic size and the node spacing of a quadtree sub-domain ensures space adaptivity. The adaptive time-stepping accelerates the calculations further. In the framework of previous research studies, we used the approach to solve quantitative phase-field models for single dendrite growth in pure melts and dilute binary alloys. In the present study, we upgrade the solution procedure for the modelling growth of multiple differently oriented dendrites. Along with the space-time adaptive approach, we apply non-linear preconditioning of the phase-field equation to increase computational efficiency. We investigate a novel numerical approach’s accuracy and computational efficiency by simulating the equiaxed dendrite growth from a dilute binary alloy.

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“…The inspiration for the development of such an approach is twofold. First, previous research (Dobravec et al , 2020, 2022) has demonstrated that using the domain-type meshless RBF-FD method in combination with space-time adaptive approach ensures high accuracy and computational efficiency for solving PF and energy conservation equations. Second, the solution of the Stokes flow around an obstacle using the boundary-type meshless method MRSM (Rek et al , 2021) is computationally much less demanding than the traditional approaches for solving momentum and mass conservation equations (Beckermann et al , 1999; Jeong et al , 2001).…”

Section: Introductionmentioning

confidence: 99%

A coupled domain–boundary type meshless method for phase-field modelling of dendritic solidification with the fluid flow

Dobravec

Mavrič

Zahoor

et al. 2023

HFF

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Purpose This study aims to simulate the dendritic growth in Stokes flow by iteratively coupling a domain and boundary type meshless method. Design/methodology/approach A preconditioned phase-field model for dendritic solidification of a pure supercooled melt is solved by the strong-form space-time adaptive approach based on dynamic quadtree domain decomposition. The domain-type space discretisation relies on monomial augmented polyharmonic splines interpolation. The forward Euler scheme is used for time evolution. The boundary-type meshless method solves the Stokes flow around the dendrite based on the collocation of the moving and fixed flow boundaries with the regularised Stokes flow fundamental solution. Both approaches are iteratively coupled at the moving solid–liquid interface. The solution procedure ensures computationally efficient and accurate calculations. The novel approach is numerically implemented for a 2D case. Findings The solution procedure reflects the advantages of both meshless methods. Domain one is not sensitive to the dendrite orientation and boundary one reduces the dimensionality of the flow field solution. The procedure results agree well with the reference results obtained by the classical numerical methods. Directions for selecting the appropriate free parameters which yield the highest accuracy and computational efficiency are presented. Originality/value A combination of boundary- and domain-type meshless methods is used to simulate dendritic solidification with the influence of fluid flow efficiently.

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Reduction of discretisation-induced anisotropy in the phase-field modelling of dendritic growth by meshless approach

Cited by 19 publications

References 40 publications

Phase Field Modeling of Dendritic Growth on Spherical Surfaces

Phase Field Modeling of Dendritic Growth on Spherical Surfaces

Application of a meshless space-time adaptive approach to phase-field modelling of polycrystalline solidification

A coupled domain–boundary type meshless method for phase-field modelling of dendritic solidification with the fluid flow

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