Boundary Knot Method for 2D Transient Heat Conduction Problems

SHI Jin-hong; FU Zhuo-jia; CHEN Wen

doi:10.3879/j.issn.1000-0887.2014.02.001

Volume 35 Issue 2

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Article Navigation > Applied Mathematics and Mechanics > 2014 > 35(2): 111-120

SHI Jin-hong, FU Zhuo-jia, CHEN Wen. Boundary Knot Method for 2D Transient Heat Conduction Problems[J]. Applied Mathematics and Mechanics, 2014, 35(2): 111-120. doi: 10.3879/j.issn.1000-0887.2014.02.001

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Boundary Knot Method for 2D Transient Heat Conduction Problems

doi: 10.3879/j.issn.1000-0887.2014.02.001

¹College of Mechanics and Materials, Hohai University, Nanjing 210098, P.R.China;²State Key Laboratory of HydrologyWater Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, P.R.China

Funds: The National Basic Research Program of China (973 Program)（2010CB832702）; The National Science Fund for Distinguished Young Scholars of China（11125208）; The National Natural Science Foundation of China（11372097;11302069）

Received Date: 2013-10-07
Rev Recd Date: 2013-11-19
Publish Date: 2014-02-15

Abstract

Abstract

The boundary knot method (BKM) in conjunction with the dual reciprocity method (DRM) was introduced to solve 2D transient heat conduction problems. With the finite difference scheme applied to deal with the time derivative term, the transient heat conduction equation was converted to a set of nonhomogeneous modified Helmholtz equations. Then the numerical solution to the nonhomogeneous problems was divided into two parts: the particular solution and the homogeneous solution. The DRM with few inner interpolation nodes was employed to get the particular solution, and the BKM with boundaryonly nodes used to obtain the homogeneous solution. Numerical results show that the present combined method has the merits of high accuracy, wide applicability, good stability and rapid convergence, which were appealing to solving transient heat conduction problems.
- transient heat conduction,
- boundary knot method,
- dual reciprocity method,
- difference scheme,
- modified Helmholtz equation

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References

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