Contemporary Meshfree Methods for Three Dimensional Heat Conduction Problems

Afrasiabi, Mohamadreza; Roethlin, M.; Wegener, Konrad

doi:10.1007/s11831-019-09355-7

Cited by 19 publications

(20 citation statements)

References 66 publications

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“…The constructive idea of RKPM is to enhance SPH kernels by applying a correction function ψ for recovering the consistency. Iterating the same procedure described in [35] for 3D implementations leads to a first-order consistent RKPM approximation for second derivatives, and subsequently, for the Laplace operator. If the approximation of ∂ 2 /∂x 2 for T is desired, the mathematical expression arrives at:…”

Section: Reproducing Kernel Particle Methods (Rkpm)mentioning

confidence: 99%

“…This procedure is repeated for the other spatial coordinates to find the Laplacian value by summing three individual second derivatives (in 3D). As pointed out in [35], it is quite popular to utilize a symmetric or anti-symmetric form of Equation (11) by replacing T j with [T j ± T i ].…”

Section: Reproducing Kernel Particle Methods (Rkpm)mentioning

confidence: 99%

“…whereby the fourth-order tensor B ≈ is defined for particle i: (14) in which the expanded definition of matrix C ∼ is found in [35,36], and the renormalization matrix A ∼ for particle i is computed by:…”

Section: Corrective Smoothed Particle Methods (Cspm)mentioning

confidence: 99%

“…Instead of computing the derivatives of the same SPH kernel, PSE constructs different kernels for different derivatives independently. A good review of this method can be found in [34,35]. Discretization of the three-dimensional Laplacian of T using a second-order PSE kernel reads:…”

Section: Particle Strength Exchange (Pse)mentioning

confidence: 99%

“…Originally derived by Fatehi et al [26] and recently applied to 3D heat conduction problems in [35], FMFS is another modern SPH scheme that provides a second-order consistent approximation of the Laplace operator. It computes ∇ 2 of function T via:…”

Section: Fatehi's Meshfree Scheme (Fmfs)mentioning

confidence: 99%

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3D Thermal Simulation of a Laser Drilling Process with Meshfree Methods

Afrasiabi

Wegener

2020

JMMP

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Numerical simulation of laser drilling is rapidly gaining interest in academia and industry since this process remains one of the most important and widely-used technologies in modern manufacturing. Meshfree methods such as Smoothed Particle Hydrodynamics (SPH) have proven to be successful as a numerical tool for the computation of the heat transfer and material removal associated with a laser drilling problem. Nonetheless, the vast majority of recent developments incorporate an inconsistent SPH kernel into their thermal simulations. In this paper, several enhanced schemes are implemented to address this problem by solving the heat transfer more accurately. These meshfree schemes can provide a second-order accurate discretization of the Laplace operator and abolish the inconsistency issue of the standard SPH kernels. An efficient approach is additionally suggested to handle the associated boundary conditions, which relies on the idea of the color function and particle label. The implementation is initially validated by a 3D benchmark study and then applied for the first time to a laser drilling problem.

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Section: Reproducing Kernel Particle Methods (Rkpm)mentioning

confidence: 99%

Section: Reproducing Kernel Particle Methods (Rkpm)mentioning

confidence: 99%

Section: Corrective Smoothed Particle Methods (Cspm)mentioning

confidence: 99%

Section: Particle Strength Exchange (Pse)mentioning

confidence: 99%

Section: Fatehi's Meshfree Scheme (Fmfs)mentioning

confidence: 99%

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3D Thermal Simulation of a Laser Drilling Process with Meshfree Methods

Afrasiabi

Wegener

2020

JMMP

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Simulation of the ductile machining mode of silicon

Klippel

Süssmaier

Röthlin

et al. 2021

Int J Adv Manuf Technol

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Diamond wire sawing has been developed to reduce the cutting loss when cutting silicon wafers from ingots. The surface of silicon solar cells must be flawless in order to achieve the highest possible efficiency. However, the surface is damaged during sawing. The extent of the damage depends primarily on the material removal mode. Under certain conditions, the generally brittle material can be machined in ductile mode, whereby considerably fewer cracks occur in the surface than with brittle material removal. In the presented paper, a numerical model is developed in order to support the optimisation of the machining process regarding the transition between ductile and brittle material removal. The simulations are performed with an GPU-accelerated in-house developed code using mesh-free methods which easily handle large deformations while classic methods like FEM would require intensive remeshing. The Johnson-Cook flow stress model is implemented and used to evaluate the applicability of a model for ductile material behaviour in the transition zone between ductile and brittle removal mode. The simulation results are compared with results obtained from single grain scratch experiments using a real, non-idealised grain geometry as present in the diamond wire sawing process.

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A Class of Mesh-Free Algorithms for Some Problems Arising in Finance and Machine Learning

LeFloch

Jean-Marc²

2023

J Sci Comput

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Contemporary Meshfree Methods for Three Dimensional Heat Conduction Problems

Cited by 19 publications

References 66 publications

3D Thermal Simulation of a Laser Drilling Process with Meshfree Methods

3D Thermal Simulation of a Laser Drilling Process with Meshfree Methods

Simulation of the ductile machining mode of silicon

A Class of Mesh-Free Algorithms for Some Problems Arising in Finance and Machine Learning

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