Analysis of variable coefficient advection–diffusion problems via complex variable reproducing kernel particle method

doi:10.1088/1674-1056/22/9/090204

中国物理B ›› 2013, Vol. 22 ›› Issue (9): 90204-090204.doi: 10.1088/1674-1056/22/9/090204

Analysis of variable coefficient advection–diffusion problems via complex variable reproducing kernel particle method

翁云杰^{a b}, 程玉民^a

a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China;
b Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China

收稿日期:2012-12-16 修回日期:2013-02-26 出版日期:2013-07-26 发布日期:2013-07-26
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11171208) and the Leading Academic Discipline Project of Shanghai City, China (Grant No. S30106).

Analysis of variable coefficient advection–diffusion problems via complex variable reproducing kernel particle method

Weng Yun-Jie (翁云杰)^{a b}, Cheng Yu-Min (程玉民)^a

a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China;
b Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China

Received:2012-12-16 Revised:2013-02-26 Online:2013-07-26 Published:2013-07-26
Contact: Cheng Yu-Min E-mail:ymcheng@shu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11171208) and the Leading Academic Discipline Project of Shanghai City, China (Grant No. S30106).

摘要/Abstract

摘要： The complex variable reproducing kernel particle method (CVRKPM) of solving two-dimensional variable coefficient advection-diffusion problems is presented in this paper. The advantage of the CVRKPM is that the shape function of a two-dimensional problem is formed with a one-dimensional basis function. The Galerkin weak form is employed to obtain the discretized system equation, and the penalty method is used to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional variable coefficient advection-diffusion problems are obtained. Two numerical examples are given to show that the method in this paper has greater accuracy and computational efficiency than the conventional meshless method such as reproducing the kernel particle method (RKPM) and the element-free Galerkin (EFG) method.

关键词: meshless method, reproducing kernel particle method (RKPM), complex variable reproducing kernel particle method (CVRKPM), advection-diffusion problem

Abstract: The complex variable reproducing kernel particle method (CVRKPM) of solving two-dimensional variable coefficient advection-diffusion problems is presented in this paper. The advantage of the CVRKPM is that the shape function of a two-dimensional problem is formed with a one-dimensional basis function. The Galerkin weak form is employed to obtain the discretized system equation, and the penalty method is used to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional variable coefficient advection-diffusion problems are obtained. Two numerical examples are given to show that the method in this paper has greater accuracy and computational efficiency than the conventional meshless method such as reproducing the kernel particle method (RKPM) and the element-free Galerkin (EFG) method.

Key words: meshless method, reproducing kernel particle method (RKPM), complex variable reproducing kernel particle method (CVRKPM), advection-diffusion problem

中图分类号: (Numerical simulation; solution of equations)

02.60.Cb

02.60.Lj (Ordinary and partial differential equations; boundary value problems) 66.10.C- (Diffusion and thermal diffusion) 82.56.Lz (Diffusion)

翁云杰, 程玉民. Analysis of variable coefficient advection–diffusion problems via complex variable reproducing kernel particle method[J]. 中国物理B, 2013, 22(9): 90204-090204.

Weng Yun-Jie (翁云杰), Cheng Yu-Min (程玉民). Analysis of variable coefficient advection–diffusion problems via complex variable reproducing kernel particle method[J]. Chin. Phys. B, 2013, 22(9): 90204-090204.

参考文献 34

[1]	Knopp T, Lube G and Rapin G 2002 Comput. Meth. Appl. Mech. Eng. 191 2997
[2]	Franca L P, Hauke G and Masud A 2006 Comput. Meth. Appl. Mech. Eng. 195 1560
[3]	John V and Knobloch P 2007 Comput. Meth. Appl. Mech. Eng. 196 2197
[4]	Turner D Z, Nakshatrala K B and Hjelmstad K D 2011 Int. J. Number. Meth. Fl. 66 64
[5]	John V and Novo J 2012 J. Comp. Phys. 231 1570
[6]	Boztosun I and Charafi A 2002 Eng. Anal. Boundary Element 26 889
[7]	Ikeuchi M and Onishi K 1983 App. Math. Model 7 115
[8]	Noye B J and Tan H H 1989 Int. J. Number. Meth. Fl. 9 75
[9]	Belytschko T, Krongauz Y, Organ D, Fleming M and Krysl P 1996 Comput. Meth. Appl. Mech. Eng. 139 3
[10]	Zerroukat M, Power H and Chen C S 1998 Int. Number. Meth. Eng. 42 1263
[11]	Zhan Z, Liew K M, Chen Y M and Lee Y Y 2008 Eng. Anal. Boundary Elements 32 241
[12]	Zhang Z, Liew K M and Cheng Y M 2008 Eng. Anal. Boundary Elements 32 241
[13]	Cheng R J and Ge H X 2009 Chin. Phys. B 18 4059
[14]	Wang J F, Sun F X and Cheng Y M 2012 Chin. Phys. B 21 090204
[15]	Ren H P and Cheng Y M 2012 Int. J. Comput. Mater. Sci. Eng. 1 1250011
[16]	Zhang Z, Li D M, Chen Y M and Liew K M 2012 Acta Mech. Sin. 28 808
[17]	Cheng R J and Ge H X 2012 Chin. Phys. B 21 040203
[18]	Qin Y X and Cheng Y M 2006 Acta Phys. Sin. 55 3215 (in Chinese)
[19]	Qin Y X and Chen Y M 2008 Chin. J. Mech. Eng. 44 95 (in Chinese)
[20]	Li Z H, Qin Y X and Cui X C 2012 Acta Phys. Sin. 61 080205 (in Chinese)
[21]	Cheng Y M and Li J H 2005 Acta Phys. Sin. 54 4463 (in Chinese)
[22]	Chen Y M, Peng M J and Li J H 2005 Acta Mech. Sin. 37 719 (in Chinese)
[23]	Peng M J, Liu P and Chen Y M 2009 Int. J. App. Mech 1 367
[24]	Liu P, Peng J and Cheng Y M 2009 Compu. Aided Eng. 18 11 (in Chinese)
[25]	Liew K M and Chen Y M 2009 Comput. Met. Appl. Mech Eng. 198 3925
[26]	Peng M J, Li D M and Chen Y M 2011 Eng. Struct. 33 127
[27]	Cheng Y M, Wang J F and Bai F N 2012 Chin. Phys. B 21 090203
[28]	Cheng Y M, Li R X and Peng M J 2012 Chin. Phys. B 21 090205
[29]	Cheng Y M, Wang J F and Li R X 2012 Int. J. Appl. Mech. 4 1250042
[30]	Yang X L, Dai and Li Z F 2012 Acta Phys. Sin. 61 050204 (in Chinese)
[31]	Chen L and Cheng Y M 2008 Acta Phys. Sin. 5 6047 (in Chinese)
[32]	Chen L and Cheng Y M 2010 Sci. China Phys Mech. Astron 53 954
[33]	Chen L and Cheng Y M 2010 Chin. Phys. B 19 090204
[34]	Chen L, Liew K M and Cheng Y M 2010 Interaction and Multiscale Mechanics: An International Journal 27

Analysis of variable coefficient advection–diffusion problems via complex variable reproducing kernel particle method

Analysis of variable coefficient advection–diffusion problems via complex variable reproducing kernel particle method

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 34

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	马吉超, 魏高峰, 刘丹丹. Improved reproducing kernel particle method for piezoelectric materials[J]. 中国物理B, 2018, 27(1): 10201-010201.
[2]	吴意, 马永其, 冯伟, 程玉民. Topology optimization using the improved element-free Galerkin method for elasticity[J]. 中国物理B, 2017, 26(8): 80203-080203.
[3]	唐耀宗, 李小林. Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems[J]. 中国物理B, 2017, 26(3): 30203-030203.
[4]	陈莘莘, 王娟, 李庆华. Two-dimensional fracture analysis of piezoelectric material based on the scaled boundary node method[J]. 中国物理B, 2016, 25(4): 40203-040203.
[5]	程荣军, 程玉民. Solving unsteady Schrödinger equation using the improved element-free Galerkin method[J]. 中国物理B, 2016, 25(2): 20203-020203.
[6]	马永其, 周延凯. Hybrid natural element method for large deformation elastoplasticity problems[J]. 中国物理B, 2015, 24(3): 30204-030204.
[7]	程玉民, 刘超, 白福浓, 彭妙娟. Analysis of elastoplasticity problems using an improved complex variable element-free Galerkin method[J]. 中国物理B, 2015, 24(10): 100202-100202.
[8]	周延凯, 马永其, 董轶, 冯伟. Hybrid natural element method for viscoelasticity problems[J]. , 2015, 24(1): 10204-010204.
[9]	王延冲, 李小林. A meshless algorithm with moving least square approximations for elliptic Signorini problems[J]. , 2014, 23(9): 90202-090202.
[10]	葛红霞, 程荣军. A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation[J]. 中国物理B, 2014, 23(4): 40203-040203.
[11]	李小林, 李淑玲. A meshless Galerkin method with moving least square approximations for infinite elastic solids[J]. 中国物理B, 2013, 22(8): 80204-080204.
[12]	王启防, 戴保东, 栗振锋. A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems[J]. 中国物理B, 2013, 22(8): 80203-080203.
[13]	Cheng Rong-Jun, Wei Qi. Analysis of the generalized Camassa and Holm equation with the improved element-free Galerkin method[J]. 中国物理B, 2013, 22(6): 60209-060209.
[14]	时婷玉, 程荣军, 葛红霞. An element-free Galerkin (EFG) method for generalized Fisher equations (GFE)[J]. 中国物理B, 2013, 22(6): 60210-060210.
[15]	王健菲, 程玉民. A new complex variable meshless method for advection–diffusion problems[J]. 中国物理B, 2013, 22(3): 30208-030208.