High precision simulation and analysis of non-Fourier heat transfer during laser processing

Xu, Bing‐Bing; Gao, Xiao‐Wei; Cui, Miao

doi:10.1016/j.ijheatmasstransfer.2021.121574

Cited by 19 publications

(5 citation statements)

References 39 publications

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“…where {u} is a vector consisting of all points u, and {f} is a known vector formed by eqn (13) or (16) and the source term s in eqn (15). By solving eqn (17), we can obtain the values of u at all points.…”

Section: Finite Line Methods For Solving Convection-diffusion Equationsmentioning

confidence: 99%

“…To overcome these drawbacks in stability, accuracy and suitability of irregular geometries, Gao et al [15] proposed a new type of collocation method, called the free element method (FrEM), which absorbs the advantages of FEM in stability, FDM in easy use and MFM in suitability for complicated geometries. FrEM has been successfully used to solve heat conduction [16], piezoelectric [17], solid mechanics [18] and fluid mechanics [19] problems. However, when using high-order free elements in FrEM, a lot of element nodes are required.…”

Section: Introductionmentioning

confidence: 99%

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Finite Line Method for Solving Convection–diffusion Equations

Gao

LIU

DING

2022

WIT Transactions on Engineering Sciences

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In this paper, a creative collocation-type numerical method, the Finite Line Method (FLM), is proposed for solving general convection-diffusion equations. The method is based on the use of a finite number of lines crossing each collocation point, and the Lagrange polynomial interpolation formulation to construct the shape functions over each line. The directional derivative technique is proposed to derive the first-order partial derivatives of any physical variables with respect to the global coordinates for the high-dimensional problems from the lines' ones and the high-order derivatives are evaluated from a recurrence formulation. The derived spatial partial derivatives are directly substituted into the governing partial differential equations and related boundary conditions of the convection-diffusion equations to set up the system of equations. The finite number of lines crossing each collocation point is called the line set. To evaluate the convection and diffusion terms accurately, two different line sets are used for these two terms, which are called the convection line set and central line set, respectively. The former is formed according to the velocity direction and is used for performing the upwind scheme in the computation of the convection term, and the latter is formed by the crossed lines including the collocation point at the center. A numerical example will be given to verify the correctness and stability of the proposed method.

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Section: Finite Line Methods For Solving Convection-diffusion Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finite Line Method for Solving Convection–diffusion Equations

Gao

LIU

DING

2022

WIT Transactions on Engineering Sciences

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“…In each sub‐domain,

{M}_{\xi}\times {M}_{\eta }

nodes in total are distributed where

{M}_{\xi },{M}_{\eta }

are the numbers of nodes along the different directions in the sub‐domain and for any collocation node

{x}^a

, a local collocation element with

{K}_{\xi}\times {K}_{\eta }

nodes can be constructed based on the collocation node and the surrounding nodes. In general, the uniform node distribution and the Chebyshev–Gauss–Lobatto node distribution 36 can be selected. Obviously, the uniformly distributed nodes are the most comfortable ones in the proposed technique.…”

Section: Domain Decomposition and Mapping Techniquementioning

confidence: 99%

Petrov–Galerkin zonal free element method for 2D and 3D mechanical problems

Gao

2023

Numerical Meth Engineering

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In this article, a novel weak‐form zonal Petrov–Galerkin free element method is proposed for two‐ and three‐dimensional linear mechanical problems. By absorbing the advantages of finite block method and strong‐form finite element method, the block mapping technique is used in the free element method. Combining the characteristics of the meshless local Petrov–Galerkin method, the local Petrov–Galerkin formulation based on the zonal free element method is formed at last. Besides, the local integral domain selected in the local collocation element is circular or spherical to simplify programming. The transformation of the local integral domain between the physical and normalized spaces is given for two‐ and three‐dimensional problems. The comparison of accuracy and convergence between the new proposed Petrov–Galerkin method and the conventional methods is carried out. Some challenging examples including fracture mechanics problems and a complex 3D problem are given to validate the convergence and accuracy of the proposed method.

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“…Based on the DPL model, Majchrzak [32] calculated the internal thermal processes of cylindrical microdomains (Cr, Au) under the action of an ultra-short laser pulse and introduced the numerical model of the melting and re-solidification of the materials. Xu et al [33] proposed an effective numerical method to solve the complexity of DPL equations. The 1-D, 2-D and 3-D models in single-phase media under laser pulse were numerically simulated.…”

Section: Introductionmentioning

confidence: 99%

Non-Fourier Heat Conduction of Nano-Films under Ultra-Fast Laser

Mao

Liu

et al. 2023

Materials

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The ultra-fast laser heating process of nano-films is characterized by an ultra-short duration and ultra-small space size, in which the classical Fourier law based on the hypothesis of local equilibrium is no longer applicable. Based on the Cattaneo–Vernotte (CV) model and the dual-phase-lag (DPL) model, the two-dimensional analytical solutions of heat conduction in nano-films under ultra-fast laser are obtained using the integral transformation method. The results show that there is a thermal wave phenomenon inside the film, which becomes increasingly evident as the elapse of the lag time of the temperature gradient. Moreover, the wave amplitude in the vertical direction is much larger than that in the horizontal direction of the nano-film. By comparing the numerical result of the two models, it is found that the temperature distribution inside the nano-film based on the DPL model is gentler than that of the CV model. Additionally, the temperature distribution in the two-dimensional solution is lower than that in the one-dimensional solution under the same Knudsen number. In the comparison results of the CV model, the maximum peak difference in the thermal wave reaches 75.08 K when the Knudsen number is 1.0. This demonstrates that the horizontal energy carried by the laser source significantly impacts the temperature distribution within the film.

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High precision simulation and analysis of non-Fourier heat transfer during laser processing

Cited by 19 publications

References 39 publications

Finite Line Method for Solving Convection–diffusion Equations

Finite Line Method for Solving Convection–diffusion Equations

Petrov–Galerkin zonal free element method for 2D and 3D mechanical problems

Non-Fourier Heat Conduction of Nano-Films under Ultra-Fast Laser

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