Three-dimensional transient heat conduction analysis by boundary knot method

Fu, Zhuojia; Shi, Jin-hong; Yang, Li-Wen

doi:10.1016/j.matcom.2018.11.025

Cited by 9 publications

(4 citation statements)

References 28 publications

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“…As we all know, there are many kinds of radial basis functions. The present study adopts the following function [28]:…”

Section: Dual Reciprocity Methodsmentioning

confidence: 99%

“…The thermal diffusivity is assumed to be a = k/ρc = 0.16 m 2 /s. The heat generation is expressed as [28] The analytical solution is given by…”

Section: Example 2: a Cube With Heat Generationmentioning

confidence: 99%

“…In order to get rid of the complexity of mesh generation and reduce the time of preprocessing, various meshless methods have devoted considerable attention. These approaches include the elementfree Galerkin method [8][9][10][11], the reproducing kernel particle method [12][13][14][15], the meshless local Petrov-Galerkin method [16,17], the radial basis function collocation method (RBFCM) [18,19], the generalized finite difference method (GFDM) [20][21][22][23], the singular boundary method (SBM) [24,25], the method of fundamental solutions (MFS) [26,27] and the boundary knot method (BKM) [28,29], etc. The successful application of these meshless methods fully demonstrates their development prospect.…”

Section: Introductionmentioning

confidence: 99%

“…Secondly, the solution of transformed equation is decomposed into a particular solution and a homogeneous solution of the corresponding homogeneous equation. Finally, the particular solution and the homogeneous solution are obtained by the dual reciprocity method (DRM) [28,45] and the LKM, respectively. The particular solution only satisfies the non-homogeneous equation, rather than boundary condition.…”

Section: Introductionmentioning

confidence: 99%

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A Novel Localized Meshless Method for Solving Transient Heat Conduction Problems in Complicated Domains

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This paper first attempts to solve the transient heat conduction problem by combining the recently proposed local knot method (LKM) with the dual reciprocity method (DRM). Firstly, the temporal derivative is discretized by a finite difference scheme, and thus the governing equation of transient heat transfer is transformed into a non-homogeneous modified Helmholtz equation. Secondly, the solution of the non-homogeneous modified Helmholtz equation is decomposed into a particular solution and a homogeneous solution. And then, the DRM and LKM are used to solve the particular solution of the non-homogeneous equation and the homogeneous solution of the modified Helmholtz equation, respectively. The LKM is a recently proposed local radial basis function collocation method with the merits of being simple, accurate, and free of mesh and integration. Compared with the traditional domain-type and boundary-type schemes, the present coupling algorithm could be treated as a really good alternative for the analysis of transient heat conduction on high-dimensional and complicated domains. Numerical experiments, including two-and three-dimensional heat transfer models, demonstrated the effectiveness and accuracy of the new methodology.

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“…As we all know, there are many kinds of radial basis functions. The present study adopts the following function [28]:…”

Section: Dual Reciprocity Methodsmentioning

confidence: 99%

“…The thermal diffusivity is assumed to be a = k/ρc = 0.16 m 2 /s. The heat generation is expressed as [28] The analytical solution is given by…”

Section: Example 2: a Cube With Heat Generationmentioning

confidence: 99%