Acceleration of RBF-FD meshless phase-field modelling of dendritic solidification by space-time adaptive approach

Dobravec, Tadej; Mavrič, Boštjan; Šarler, Božidar

doi:10.1016/j.camwa.2022.09.008

Cited by 16 publications

(28 citation statements)

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“…Solution procedure 3.1. Solution of governing equations for ψ and U We solve the governing equations for ψ and U by our previously developed space-time adaptive approach [7]. It is based on dynamic quadtree domain decomposition, as seen in figure 1.…”

Section: Anisotropy Of the Surface Energymentioning

confidence: 99%

“…The constant ratio m Ω between a quadtree sub-domain's side length and node spacing ensures space adaptivity, as seen on the left in figure 1. The free parameters of the space-time adaptive approach are the minimum spacing h, the ratio m Ω , the maximum number of different node spacings n h , the maximum number of different time steps n ∆t , and the overlapping parameter n overlap [7]. In this paper, we set n overlap = 1 and n ∆t = 2; such configuration yields good accuracy and computational efficiency [7].…”

Section: Anisotropy Of the Surface Energymentioning

confidence: 99%

“…The free parameters of the space-time adaptive approach are the minimum spacing h, the ratio m Ω , the maximum number of different node spacings n h , the maximum number of different time steps n ∆t , and the overlapping parameter n overlap [7]. In this paper, we set n overlap = 1 and n ∆t = 2; such configuration yields good accuracy and computational efficiency [7]. In subsection 4.1, we analyse the influence of minimum spacing h on the accuracy.…”

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%

“…Researchers developed many different computational approaches for the PF modelling of dendritic growth in the last 20 years, e.g., adaptive mesh refinement [22], parallel simulations using graphic processing units [23], implicit time-stepping and multi-grid approaches [24], etc. In this paper, we employ the space-time adaptive algorithm to accelerate the meshless PF modelling of dendritic solidification [7]. Meshless methods represent a fast-growing family of numerical methods that do not rely on the division in space in elements like finite element or finite volume methods.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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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Section: Anisotropy Of the Surface Energymentioning

confidence: 99%

Section: Anisotropy Of the Surface Energymentioning

confidence: 99%