[1]余闯,方冬芳,杜广印,等.土介质中污染物迁移模型的同伦分析解[J].东南大学学报(自然科学版),2015,45(6):1185-1189.[doi:10.3969/j.issn.1001-0505.2015.06.029]
 Yu Chuang,Fang Dongfang,Du Guangyin,et al.Homotopy analysis solutions of contaminant transport model in soil medium[J].Journal of Southeast University (Natural Science Edition),2015,45(6):1185-1189.[doi:10.3969/j.issn.1001-0505.2015.06.029]
点击复制

土介质中污染物迁移模型的同伦分析解()
分享到:

《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
45
期数:
2015年第6期
页码:
1185-1189
栏目:
计算机科学与工程
出版日期:
2015-11-20

文章信息/Info

Title:
Homotopy analysis solutions of contaminant transport model in soil medium
作者:
余闯1方冬芳2杜广印3蔡晓庆1温灿灿2杨萌2
1温州大学建筑工程学院, 温州 325035; 2温州大学数学与信息科学学院, 温州 325035; 3东南大学交通学院, 南京 210096
Author(s):
Yu Chuang1 Fang Dongfang2 Du Guangyin3 Cai Xiaoqing1 Wen Cancan2 Yang Meng2
1College of Civil Engineering and Architecture, Wenzhou University, Wenzhou 325035, China
2College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China
3School of Transportation, Southeast University, Nanjing 210096, China
关键词:
同伦分析法 污染物 迁移 降解 初始条件
Keywords:
homotopy analysis method contaminant transport decay initial condition
分类号:
TP309
DOI:
10.3969/j.issn.1001-0505.2015.06.029
摘要:
针对现有解析方法的局限性,引入同伦分析法求解土介质中污染物迁移问题.通过选取辅助线性算子和非线性算子,构造零阶形变方程,编制了计算程序.应用同伦分析法求解了具有一般初始条件的恒源浓度下考虑污染物降解作用的对流-扩散模型,获得的解答与精确解吻合良好,证明了该方法的正确性.然后将同伦分析法推广到求解考虑源浓度随时间按指数衰减的一维污染物迁移模型,克服了常规方法难以直接求解的缺陷,获得了污染物浓度随时间和空间变化的理论解答.实例计算表明,同伦分析法可以求解具有更一般初始条件的复杂的污染物迁移模型,并且数学概念清楚、计算简便,是研究污染物迁移问题的一种有效方法.
Abstract:
Due to the limitations of the existing analytical methods, the homotopy analysis method(HAM)is implemented to solve the contaminant transport model in soil medium. With the auxiliary linear operator and the nonlinear operator, the zero order deformation equation is proposed and the computation program is compiled. By using the HAM, the advection-diffusion model considering decay is solved at a fixed contaminant concentration under general initial conditions. The computation solution is in good agreement with the exact solution, which proves the correctness of the proposed method. Then, the HAM is applied to solve the one-dimensional contaminant transport model considering the exponential decay of the source concentration with time, which overcomes the difficulty in direct solution of the general methods, and the theoretical solutions of the contaminant concentration changing with time and space are obtained. Case study results show that the HAM, with clear concept and simple computation, can be used for contaminant transport models under general and complex initial conditions and owes, which is one of the most effective methods for research in the contaminant transport issue.

参考文献/References:

[1] 陈云敏.环境土工基本理论及工程应用[J]. 岩土工程学报,2014,36(1): 1-46.
  Chen Yunmin. A fundamental theory of environmental geotechnics and its application [J].Chinese Journal of Geotechnical Engineering, 2014, 36(1): 1-46.(in Chinese)
[2] 陈云敏, 谢海建, 柯瀚, 等. 挥发性有机化合物在复合衬里中的一维扩散解[J]. 岩土工程学报,2006,28(9):1076-1080.
  Chen Yunmin, Xie Haijian, Ke Han, et al. Analytical solution of one-dimensional diffusion of volatile organic compounds(VOCs)through composite liners[J]. Chinese Journal of Geotechnical Engineering, 2006, 28(9): 1076-1080.(in Chinese)
[3] 陈云敏,谢海建,柯瀚,等.层状土中污染物的一维扩散解析解[J].岩土工程学报,2006,28(4): 521-524.
  Chen Yunmin, Xie Haijian, Ke Han, et al. Analytical solution of contaminant diffusion through multi-layered soils[J]. Chinese Journal of Geotechnical Engineering, 2006, 28(4): 521-524.(in Chinese)
[4] 余闯,方冬芳,杜广印,等. 均质土中考虑溶质蜕变效应的污染物迁移模型的解析解[J].东南大学学报:自然科学版, 2012, 42(6): 1206-1210.
  Yu Chuang, Fang Dongfang, Du Guangyin, et al. Analytical solution on pollutant migration considering solute decay in homogeneous soil [J]. Journal of Southeast University:Natural Science Edition, 2012, 42(6): 1206-1210.(in Chinese)
[5] 张文杰,黄依艺,张改革.填埋场污染物在有限厚度土层中一维对流-扩散-吸附解析解[J].岩土工程学报,2013, 35(7): 1197-1201.
  Zhang Wenjie, Huang Yiyi, Zhang Gaige. Analytical solution of 1D advection-diffusion-adsorption transport of landfill contaminants through a soil layer with finite thickness [J]. Chinese Journal of Geotechnical Engineering, 2013, 35(7): 1197-1201.(in Chinese)
[6] Chakraborty R, Ghosh A. Finite difference method for computation of 1D pollutant migration through saturated homogeneous soil media[J].International Journal of Geomechanics,2011,11(1):12-22.
[7] van Genuchten M T, Alves W J. Analytical solutions of the one-dimensional convective-dispersive solute transport equation [R].Washington DC, USA: United States Department of Agriculture, 1982.
[8] Williams G P, Tomasko D. Analytical solution to the advective-dispersive equation with a decaying source and contaminant[J].Journal of Hydrologic Engineering, 2008, 13(12):1193-1196.
[9] Chen C-K, Ju S-P. Application of differential transformation to transient advective-dispersive transport equation [J].Applied Mathematics and Computation, 2004, 155(1): 25-38.
[10] 谢海建,柯瀚,陈云敏. 浓度变化时复合衬层中有机污染物的一维扩散分析[J]. 环境科学学报,2006,26(6):930-935.
  Xie Haijian, Ke Han, Chen Yunmin. Analysis of one-dimensional organic contaminants diffusion through composite liner under time-dependent concentration conditions[J]. Acta Scientiae Circumstantiae, 2006, 26(6): 930-935.(in Chinese)
[11] Simpson M J, Ellery A J.Exact series solutions of reactive transport models with general initial conditions [J]. Journal of Hydrology, 2014, 513: 7-12.
[12] 廖世俊,陈晨,徐航.超越摄动-同伦分析方法导论[M].北京:科学出版社,2006:1-10.
[13] Liao S J. An approximate solution technique which does not depend upon small parameters: a special example [J].International Journal of Non-Linear Mechanica, 1995, 30(3):371-380.

相似文献/References:

[1]杨小丽,王世和,卢宁.膜生物反应器净化污水的抗冲击性能[J].东南大学学报(自然科学版),2005,35(5):797.[doi:10.3969/j.issn.1001-0505.2005.05.030]
 Yang Xiaoli,Wang Shihe,Lu Ning.Impact of shock loading on membrane bioreactor for sewage treatment[J].Journal of Southeast University (Natural Science Edition),2005,35(6):797.[doi:10.3969/j.issn.1001-0505.2005.05.030]
[2]胡启洲,吴鹏,邓卫,等.车辆排放对大气污染的综合测度模型[J].东南大学学报(自然科学版),2016,46(4):884.[doi:10.3969/j.issn.1001-0505.2016.04.035]
 Hu Qizhou,Wu Peng,Deng Wei,et al.Comprehensive measure model for air pollution due to vehicle emissions[J].Journal of Southeast University (Natural Science Edition),2016,46(6):884.[doi:10.3969/j.issn.1001-0505.2016.04.035]
[3]胡启洲,邓卫,李晓菡.城市道路车辆排放对大气污染的线性诊断模型[J].东南大学学报(自然科学版),2018,48(5):967.[doi:10.3969/j.issn.1001-0505.2018.05.028]
 Hu Qizhou,Deng Wei,Li Xiaohan.Linear diagnosis model of vehicle emission to air pollution on urban road[J].Journal of Southeast University (Natural Science Edition),2018,48(6):967.[doi:10.3969/j.issn.1001-0505.2018.05.028]

备注/Memo

备注/Memo:
收稿日期: 2015-03-28.
作者简介: 余闯(1977—),男,博士,教授,geoyuchuang@163.com.
基金项目: 国家自然科学基金资助项目(41372264,51508418,51578427)、浙江省自然科学基金资助项目(LY13E080013)、浙江省公益性技术应用研究计划资助项目(2014C33015,2015C33220).
引用本文: 余闯,方冬芳,杜广印,等.土介质中污染物迁移模型的同伦分析解[J].东南大学学报:自然科学版,2015,45(6):1185-1189. [doi:10.3969/j.issn.1001-0505.2015.06.029]
更新日期/Last Update: 2015-11-20