A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems

doi:10.1088/1674-1056/22/8/080203

Abstract On the basis of the complex variable moving least-square (CVMLS) approximation, a complex variable meshless local Petrov-Galerkin (CVMLPG) method is presented for transient heat conduction problems. The method is developed based on the CVMLS approximation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each sub-domain to avoid the need for a domain integral in symmetric weak form. In the construction of the well-performed shape function, the trial function of a two-dimensional (2D) problem is formed with a one-dimensional (1D) basis function, thus improving computational efficiency. The numerical results are compared with the exact solutions of the problems and the finite element method (FEM). This comparison illustrates the accuracy as well as the capability of the CVMLPG method.

Keywords: meshless method complex variable moving least-square method complex variable meshless local Petrov-Galerkin method transient heat conduction problems

Received: 28 January 2013
Revised: 28 March 2013
Accepted manuscript online:

PACS:	02.60.Cb	(Numerical simulation; solution of equations)
	02.60.Lj	(Ordinary and partial differential equations; boundary value problems)
	44.10.+i	(Heat conduction)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 51078250), the Research Project by Shanxi Scholarship Council of Shanxi Province, China (Grant No. 2013-096), and the Scientific & Technological Innovation Program for Postgraduates of Taiyuan University of Science and Technology, China (Grant No. 20125026).

Corresponding Authors: Dai Bao-Dong
E-mail: Dai_baodong@126.com

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Wang Qi-Fang (王启防), Dai Bao-Dong (戴保东), Li Zhen-Feng (栗振锋) A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems 2013 Chin. Phys. B 22 080203

[1]	Zhang X, Liu Y and Ma S 2009 Adv. Mech. 39 1
[2]	Atluri S N and Zhu T L 1998 Comput. Mech. 22 117
[3]	Ching H K and Batra R C 2001 Comput. Model. Eng. Sci. 2 273
[4]	Long S Y and Atluri S N 2002 Comput. Model. Eng. Sci. 3 53
[5]	Han Z D, Rajendran A M and Atluri S N 2005 Comput. Model. Eng. Sci. 10 1
[6]	Wu X H and Tao W Q 2008 Int. J. Heat Mass Transfer 51 3103
[7]	Lin H and Atluri S N 2001 Comput. Model. Eng. Sci. 2 117
[8]	Liew K M, Feng C, Cheng Y and Kitipornchai S 2007 Int. J. Numer. Meth. Eng. 70 46
[9]	Cheng Y M, Peng M J and Li J H 2005 Chin. J. Theor. Appl. Mech. 37 1
[10]	Peng M J, Liu P and Cheng Y M 2009 Int. J. Appl. Mech. 1 367
[11]	Bai F N, Li D M, Wang J F and Cheng Y M 2012 Chin. Phys. B 21 020204
[12]	Peng M J, Li D M and Cheng Y M 2011 Engin. Struct. 33 127
[13]	Li D M, Bai F N, Cheng Y M and Liew K M 2012 Comp. Meth. Appl. Mech. Eng. 233-236 1
[14]	Cheng Y M, Li R X and Peng M J 2012 Chin. Phys. B 21 090205
[15]	Wang J F and Cheng Y M 2012 Chin. Phys. B 21 120206
[16]	Cheng Y M, Wang J F and Li R X 2012 Int. J. Appl. Mech. 4 1250042
[17]	Cheng Y M, Wang J F and Bai F N 2012 Chin. Phys. B 21 090203
[18]	Wang J F and Cheng Y M 2013 Chin. Phys. B 22 030208
[19]	Liew K M and Cheng Y M 2009 Comp. Meth. Appl. Mech. Eng. 198 3925
[20]	Yang X L, Dai B D and Li Z F 2012 Acta Phys. Sin. 61 050204 (in Chinese)
[21]	Yang X L, Dai B D and Zhang W W 2012 Chin. Phys. B 21 100208
[22]	Gao H F and Cheng Y M 2009 Chin. J. Theor. Appl. Mech. 41 480
[23]	Gao H F and Cheng Y M 2010 Int. J. Comput. Meth. 7 55
[24]	Chen L and Cheng Y M 2008 Acta Phys. Sin. 57 1 (in Chinese)
[25]	Chen L and Cheng Y M 2008 Acta Phys. Sin. 57 6047 (in Chinese)
[26]	Chen L and Cheng Y M 2010 Chin. Phys. B 19 090204
[27]	Chen L and Cheng Y M 2010 Sci. China G: Phys. Mech. Astron. 40 242
[28]	Li Q H, Chen S S and Kou G X 2011 J. Comput. Phys. 230 2739

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A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems

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