Please wait a minute...
Chin. Phys. B, 2012, Vol. 21(12): 120206    DOI: 10.1088/1674-1056/21/12/120206
GENERAL Prev   Next  

A new complex variable meshless method for transient heat conduction problems

Wang Jian-Fei (王健菲)a b, Cheng Yu-Min (程玉民)a b
a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
b Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China
Abstract  In this paper, based on the improved complex variable moving least-square (ICVMLS) approximation, a new complex variable meshless method (CVMM) for two-dimensional (2D) transient heat conduction problems is presented. The variational method is employed to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. As the transient heat conduction problems are related to time, Crank-Nicolson difference scheme for two-point boundary value problems is selected for the time discretization. Then the corresponding formulae of the CVMM for 2D heat conduction problems are obtained. In order to demonstrate the applicability of the proposed method, numerical examples are given to show the high convergence rate, good accuracy, and high efficiency of the CVMM presented in this paper.
Keywords:  meshless method      improved complex variable moving least-square approximation      complex variable meshless method      transient heat conduction problem  
Received:  16 May 2012      Revised:  03 June 2012      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. 11171208), and the Shanghai Leading Academic Discipline Project, China (Grant No. S30106), and the Innovation Fund for Graduate Student of Shanghai University of China (Grant No. SHUCX120125).
Corresponding Authors:  Cheng Yu-Min     E-mail:  ymcheng@shu.edu.cn

Cite this article: 

Wang Jian-Fei (王健菲), Cheng Yu-Min (程玉民) A new complex variable meshless method for transient heat conduction problems 2012 Chin. Phys. B 21 120206

[1] Belytschko T, Krongauz Y, Organ D, Fleming M and Krysl P 1996 Comput. Methods Appl. Mech. Engrg. 139 3
[2] Qin Y X and Cheng Y M 2006 Acta Phys. Sin. 55 3215 (in Chinese)
[3] Cheng R J and Cheng Y M 2011 Acta Phys. Sin. 60 070206 (in Chinese)
[4] Li S C, Cheng Y M and Li S C 2006 Acta Phys. Sin. 55 4760 (in Chinese)
[5] Cheng Y and Li J 2006 Sci. Chin. G: Phys. Mech. & Astron. 49 46
[6] Li D M, Peng M J and Cheng Y M 2011 Sci. Chin.: Phys. Mech. & Astron. 41 1003 (in Chinese)
[7] Dai B D and Cheng Y M 2007 Acta Phys. Sin. 56 597 (in Chinese)
[8] Cheng R J and Cheng Y M 2008 Acta Phys. Sin. 57 6037 (in Chinese)
[9] Cheng R J and Cheng Y M 2011 Chin. Phys. B 20 070206
[10] Chen L and Cheng Y M 2010 Chin. Phys. B 19 090204
[11] Cheng Y M and Li J H 2005 Acta Phys. Sin. 54 4463 (in Chinese)
[12] Chen L and Cheng Y M 2008 Acta Phys. Sin. 57 1 (in Chinese)
[13] Lancaster P and Salkauskas K 1981 Math. Comput. 37 141
[14] Afshar M H, Naisipour M and Amani J 2011 Finite Elem. Anal. Des. 47 1315
[15] Wang J F, Bai F N and Cheng Y M 2011 Chin. Phys. B 20 030206
[16] Zhang Z, Zhao P and Liew K M 2009 Eng. Anal. Bound. Elem. 33 547
[17] Ren H P, Cheng Y M and Zhang W 2009 Chin. Phys. B 18 4065
[18] Bai F N, Li D M, Wang J F and Cheng Y M 2012 Chin. Phys. B 21 020204
[19] Cheng Y M, Peng M J and Li J H 2005 Chin. J. Theor. Appl. Mech. 37 719 (in Chinese)
[20] Arefmanesh A, Najafi M and Abdi H 2005 J. Fluid Eng. 127 647
[21] Batra R C, Porfiri M and Spinello D 2004 Int. J. Numer. Method Eng. 61 2461
[22] Liu Y, Zhang X and Lu M W 2005 Tsinghua Sci. Tech. 10 61
[23] Liu Y, Zhang X and Lu M W 2005 Numer. Heat Transfer B: Fund. 47 257
[24] Chen L and Cheng Y M 2008 Acta Phys. Sin. 57 6047 (in Chinese)
[1] Improved reproducing kernel particle method for piezoelectric materials
Ji-Chao Ma(马吉超), Gao-Feng Wei(魏高峰), Dan-Dan Liu(刘丹丹). Chin. Phys. B, 2018, 27(1): 010201.
[2] Topology optimization using the improved element-free Galerkin method for elasticity
Yi Wu(吴意), Yong-Qi Ma(马永其), Wei Feng(冯伟), Yu-Min Cheng(程玉民). Chin. Phys. B, 2017, 26(8): 080203.
[3] Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems
Yao-Zong Tang(唐耀宗), Xiao-Lin Li(李小林). Chin. Phys. B, 2017, 26(3): 030203.
[4] Two-dimensional fracture analysis of piezoelectric material based on the scaled boundary node method
Shen-Shen Chen(陈莘莘), Juan Wang(王娟), Qing-Hua Li(李庆华). Chin. Phys. B, 2016, 25(4): 040203.
[5] Solving unsteady Schrödinger equation using the improved element-free Galerkin method
Rong-Jun Cheng(程荣军) and Yu-Min Cheng(程玉民). Chin. Phys. B, 2016, 25(2): 020203.
[6] Hybrid natural element method for large deformation elastoplasticity problems
Ma Yong-Qi (马永其), Zhou Yan-Kai (周延凯). Chin. Phys. B, 2015, 24(3): 030204.
[7] Analysis of elastoplasticity problems using an improved complex variable element-free Galerkin method
Cheng Yu-Min (程玉民), Liu Chao (刘超), Bai Fu-Nong (白福浓), Peng Miao-Juan (彭妙娟). Chin. Phys. B, 2015, 24(10): 100202.
[8] Hybrid natural element method for viscoelasticity problems
Zhou Yan-Kai (周延凯), Ma Yong-Qi (马永其), Dong Yi (董轶), Feng Wei (冯伟). Chin. Phys. B, 2015, 24(1): 010204.
[9] A meshless algorithm with moving least square approximations for elliptic Signorini problems
Wang Yan-Chong (王延冲), Li Xiao-Lin (李小林). Chin. Phys. B, 2014, 23(9): 090202.
[10] A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation
Ge Hong-Xia (葛红霞), Cheng Rong-Jun (程荣军). Chin. Phys. B, 2014, 23(4): 040203.
[11] Analysis of variable coefficient advection–diffusion problems via complex variable reproducing kernel particle method
Weng Yun-Jie (翁云杰), Cheng Yu-Min (程玉民). Chin. Phys. B, 2013, 22(9): 090204.
[12] A meshless Galerkin method with moving least square approximations for infinite elastic solids
Li Xiao-Lin (李小林), Li Shu-Ling (李淑玲). Chin. Phys. B, 2013, 22(8): 080204.
[13] A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems
Wang Qi-Fang (王启防), Dai Bao-Dong (戴保东), Li Zhen-Feng (栗振锋). Chin. Phys. B, 2013, 22(8): 080203.
[14] Analysis of the generalized Camassa and Holm equation with the improved element-free Galerkin method
Cheng Rong-Jun, Wei Qi. Chin. Phys. B, 2013, 22(6): 060209.
[15] An element-free Galerkin (EFG) method for generalized Fisher equations (GFE)
Shi Ting-Yu (时婷玉), Cheng Rong-Jun (程荣军), Ge Hong-Xia (葛红霞). Chin. Phys. B, 2013, 22(6): 060210.
No Suggested Reading articles found!