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一种用于求解具有复杂边界的二维各向异性热传导问题的简单、有效且高精度的边界无网格方法。

A simple, effective and high-precision boundary meshfree method for solving 2D anisotropic heat conduction problems with complex boundaries.

作者信息

Ling Jing, Yang Dongsheng

机构信息

School of Materials and Architectural Engineering (Guizhou School of Emergency Management), Guizhou Normal University, Guiyang City, 550025, China.

Guizhou Key Laboratory of Inorganic Nonmetal Function Materials, Guizhou Normal University, Guiyang City, 550025, China.

出版信息

Sci Rep. 2024 Oct 14;14(1):23963. doi: 10.1038/s41598-024-74950-z.

DOI:10.1038/s41598-024-74950-z
PMID:39397090
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11471769/
Abstract

A simple, effective and high-precision boundary meshfree method called virtual boundary meshfree Galerkin method (VBMGM) is used to tackle 2D anisotropic heat conduction problems with complex boundaries. Temperature and heat flux are expressed by virtual boundary element method. The virtual source function is constructed through the utilization of radial basis function interpolation. Calculation model diagram and discrete model diagram of real boundaries, and schematic diagram of VBMGM are demonstrated. Using Galekin method and considering boundary conditions, the integral equation and the discrete formula of VBMGM are given in detail. The benefits of the Galerkin, meshfree, and boundary element methods are all presented in VBMGM. Seven numerical examples of general anisotropic heat conduction problems (including three numerical examples with complex boundaries and four numerical examples with mixed boundary conditions) are computed and contrasted with precise solutions and different numerical methods. The computation time of each example is given. The number of degrees of freedom used in many examples is half or less than that of the numerical method being compared. The suggested method has been demonstrated to be effective and high-precision for solving the 2D anisotropic heat conduction problems with complex boundaries.

摘要

一种简单、有效且高精度的无网格边界方法——虚拟边界无网格伽辽金法（VBMGM）被用于处理具有复杂边界的二维各向异性热传导问题。温度和热通量通过虚拟边界元法表示。虚拟源函数通过径向基函数插值构建。展示了真实边界的计算模型图和离散模型图以及VBMGM的示意图。利用伽辽金法并考虑边界条件，详细给出了VBMGM的积分方程和离散公式。伽辽金法、无网格法和边界元法的优点都体现在VBMGM中。计算了七个一般各向异性热传导问题的数值例子（包括三个具有复杂边界的数值例子和四个具有混合边界条件的数值例子），并与精确解和不同数值方法进行对比。给出了每个例子的计算时间。许多例子中使用的自由度数量是所比较数值方法的一半或更少。结果表明，所提出的方法对于求解具有复杂边界的二维各向异性热传导问题是有效且高精度的。

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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a0cd/11471769/9acde96a6078/41598_2024_74950_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a0cd/11471769/97b8afc552fc/41598_2024_74950_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a0cd/11471769/173e2cff9442/41598_2024_74950_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a0cd/11471769/a08c338c4a19/41598_2024_74950_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a0cd/11471769/5a4f1cbca769/41598_2024_74950_Fig12_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a0cd/11471769/e9467fbe14f2/41598_2024_74950_Fig13_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a0cd/11471769/09a86ced9063/41598_2024_74950_Fig14_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a0cd/11471769/e2549f23efc1/41598_2024_74950_Fig15_HTML.jpg

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