A new complex variable meshless method for advection–diffusion problems

doi:10.1088/1674-1056/22/3/030208

Abstract
Figure/Table
References (22)
Related articles (15)

Download: PDF (317 KB)
Export: BibTeX | EndNote (RIS)

Abstract In this paper, based on the improved complex variable moving least-square (ICVMLS) approximation, an improved complex variable meshless method (ICVMM) for two-dimensional advection–diffusion problems is developed. The equivalent functional of two-dimensional advection–diffusion problems is formed, the variation method is used to obtain the equation system, and the penalty method is employed to impose the essential boundary conditions. The difference method for two-point boundary value problems is used to obtain the discrete equations. Then the corresponding formulas of the ICVMM for advection–diffusion problems are presented. Two numerical examples with different node distributions are used to validate and investigate the accuracy and efficiency of the new method in this paper. It is shown that the ICVMM is very effective for advection–diffusion problems, and has good convergent character, accuracy, and computational efficiency.

Key words： meshless method improved complex variable moving least-square approximation improved complex variable meshless method advection–diffusion problem

Received: 13 August 2012

:	02.60.Cb	(Numerical simulation; solution of equations)
	02.60.Lj	(Ordinary and partial differential equations; boundary value problems)
	66.10.C-	(Diffusion and thermal diffusion)
	82.56.Lz	(Diffusion)

Fund:Project supported by the National Natural Science Foundation of China (Grant No. 11171208), the Shanghai Leading Academic Discipline Project, China (Grant No. S30106), and the Innovation Fund for Graduate Student of Shanghai University, China (Grant No. SHUCX120125).

Corresponding Authors: Cheng Yu-Min

E-mail: ymcheng@shu.edu.cn

	Service

	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	Wang Jian-Fei
	Cheng Yu-Min

Cite this article:

Wang Jian-Fei,Cheng Yu-Min. A new complex variable meshless method for advection–diffusion problems[J]. Chin. Phys. B, 2013, 22(3):030208.

URL:

http://cpb.iphy.ac.cn/EN/10.1088/1674-1056/22/3/030208 OR http://cpb.iphy.ac.cn/EN/Y2013/V22/I3/30208

[1]	Franca LP, Hauke G and Masud A 2006 Comput. Method Appl. M. 195 1560
[2]	Turner D Z, Nakshatrala K B and Hjelmstad K D 2011 Int. J. Numer. Meth. Fl. 66 64
[3]	Volker J and Petr K 2007 Comput. Method Appl. M. 196 2197
[4]	Volker J and Julia N 2012 J. Comput. Phys. 231 1570
[5]	Knopp T, Lube G and Rapin G 2002 Comput. Method Appl. M. 191 2997
[6]	Boztosun I and Charafi A 2002 Eng. Anal. Bound Elem. 26 889
[7]	Noye B J and Tan H H 1989 Int. J. Numer. Meth. Fl. 9 75
[8]	Ikeuchi M and Onishi K 1983 Appl. Math. Model. 7 115
[9]	Zerroukat M, Power H and Chen C S 1998 Int. J. Numer. Meth. Eng. 42 1263
[10]	Dai B D and Cheng Y M 2007 Acta Phys. Sin. 56 597 (in Chinese)
[11]	Zhang Z, Zhao P and Liew K M 2009 Eng. Anal. Bound. Elem. 33 547
[12]	Li S C, Cheng Y M and Li S C 2006 Acta Phys. Sin. 55 4760 (in Chinese)
[13]	Ren H P, Cheng Y M and Zhang W 2009 Chin. Phys. B 18 4065
[14]	Bai F N, Li D M, Wang J F and Cheng Y M 2012 Chin. Phys. B 21 020204
[15]	Cheng R J and Cheng Y M 2008 Acta Phys. Sin. 57 6037 (in Chinese)
[16]	Chen L and Cheng Y M 2010 Chin. Phys. B 19 090204
[17]	Cheng R J and Cheng Y M 2011 Chin. Phys. B 20 070206
[18]	Qin Y X and Cheng Y M 2006 Acta Phys. Sin. 55 3215 (in Chinese)
[19]	Zhuang P, Gu Y T and Liu F 2011 Int. J. Numer. Meth. Eng. 88 1346
[20]	Wang J F, Bai F N and Cheng Y M 2011 Chin. Phys. B 20 030206
[21]	Cheng Y M, Peng M J and Li J H 2005 Chin. J. Theor. Appl. Mech. 37 719 (in Chinese)
[22]	Belytschko T, Krongauz Y, Organ D, Fleming M and Krysl P 1996 Comput. Methods Appl. Mech. Eng. 139 3