A cellular automaton – finite volume method for the simulation of dendritic and eutectic growth in binary alloys using an adaptive mesh refinement

Dobravec, Tadej; Mavrič, Boštjan; Šarler, Božidar

doi:10.1016/j.jcp.2017.08.011

Cited by 20 publications

(3 citation statements)

References 31 publications

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“…An adaptive mesh refinement (AMR) method optimizes the numerical performance without wasting computational resources. 231–234 AMR is a powerful computational framework that is commonly applied in tracking front propagation, 235,236 dendrite growth 237–239 and interfacial flows. 240–242…”

Section: Methodsmentioning

confidence: 99%

Geometry-structure models for liquid crystal interfaces, drops and membranes: wrinkling, shape selection and dissipative shape evolution

Wang,

Servio,

Rey

2023

Soft Matter

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Section: Methodsmentioning

confidence: 99%

Geometry-structure models for liquid crystal interfaces, drops and membranes: wrinkling, shape selection and dissipative shape evolution

Wang,

Servio,

Rey

2023

Soft Matter

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“…Microstructure evolution is closely linked to material properties (Campbell, 2003); hence, one can use numerical modelling to design and optimise high-quality castings. Different approaches are used for modelling dendritic solidification, for example, the cellular automaton model (Reuther and Rettenmayr, 2014;Dobravec et al, 2017), level-set method (Gibou et al, 2003;Tan and Zabaras, 2006) and phase-field (PF) method (Chen, 2002;Boettinger et al, 2002;Dong et al, 2017;Karma and Tourret, 2016). This study uses the PF method, a powerful approach for solving various free boundary problems in materials science (Provatas and Elder, 2010;Steinbach, 2009).…”

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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“…The Local Radial Basis function Collocation Method (LRBFCM) is used for interpolation of all the unknown fields over each slice at given time and position. LRBFCM has been previously described [3], applied to simulation of fluid flow problems [4], thermo-mechanics [5], dendritic growth [6], finishing rolling mills [7]. The rest of the paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

A Rolling Simulation System for Reversing Rolling Mills

Hanoglu

Šarler

2018

MATEC Web Conf.

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In this work a rolling simulation system has been developed for rolling schedules which consists of multiple reversing rolling mills. A slice model approach is applied where the position of a slice can only be determined by considering total deformation. Each slice is parallel to each other and perpendicular to the rolling direction. The solution of coupled thermal and mechanical models over each slice, at a given time and position, are achieved by a novel meshless Local Radial Basis Function Collocation Method (LRBFCM). Mechanical material model obeys ideal plastic flow rule defined by Von Mises. Unknown fields over the slices are interpolated by a certain number of collocation points distributed over the physical domain and its boundary. A system of equations is solved for each collocation point considering its local neighbouring points in the range between 5 and 7. A non-linear system of equations is solved by direct iteration. Groove geometries of each roll are implemented in a compatible way with the slice model and every roll has a horizontal orientation. In between each rolling pass the billet is rotated either 90 or 45 degrees clockwise or counter clockwise. Reduction at each of the passes can be very high, and in such cases, the material completely fills up the groove. This requires a special attention regarding the contact boundary conditions and the collocation node distribution due to numerical instability issues. Coulomb model of friction or sticking boundary conditions are used at the contact boundaries and Gauss-Seidel iterative elliptic node generation algorithm is used for redistributing collocation nodes over the physical domain, when necessary. The simulation results for arbitrary initial position of the slice in the billet are shown in terms of temperature, displacement, strain and stress fields as well as roll forces and torques. A user friendly computer application is created for industrial use based on C# and .NET.

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A cellular automaton – finite volume method for the simulation of dendritic and eutectic growth in binary alloys using an adaptive mesh refinement

Cited by 20 publications

References 31 publications

Geometry-structure models for liquid crystal interfaces, drops and membranes: wrinkling, shape selection and dissipative shape evolution

Geometry-structure models for liquid crystal interfaces, drops and membranes: wrinkling, shape selection and dissipative shape evolution

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

A Rolling Simulation System for Reversing Rolling Mills

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