Semi-analytical solution to one-dimensional advective-dispersive-reactive transport equation using homotopy analysis method
•HAM has been applied to solve 1-D reactive transport equation.•General boundary conditions and smooth initial conditions are considered.•A convenient way is adopted to control and adjust the convergence of series solutions.•Approximate solutions produced by HAM agree well with exact solutions. The...
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| Published in | Journal of hydrology (Amsterdam) Vol. 565; pp. 422 - 428 |
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| Main Authors | , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.10.2018
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0022-1694 1879-2707 |
| DOI | 10.1016/j.jhydrol.2018.08.041 |
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| Abstract | •HAM has been applied to solve 1-D reactive transport equation.•General boundary conditions and smooth initial conditions are considered.•A convenient way is adopted to control and adjust the convergence of series solutions.•Approximate solutions produced by HAM agree well with exact solutions.
The one-dimensional advective-dispersive-reactive transport equation has been widely applied to describe the transportation process of landfill leachate through liners or anti-seepage curtains. However, most existing methods solving this problem are limited to simple initial conditions. In order to eliminate these limitations, homotopy analysis method (HAM) is implemented to solve the contaminant transport model in this paper. Applying auxiliary linear and nonlinear operator, zero order deformation equation is developed to solve contaminant transport problems numerically, with smooth initial conditions and variable source concentration being considered. HAM has been applied to simulate different contamination transport problems in one-dimensional space reported in literature. Good agreement between HAM solutions and analytical solutions has been achieved for all cases considered, demonstrating the feasibility of HAM to solve the contaminant transport model with more general, smooth initial conditions. |
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| AbstractList | •HAM has been applied to solve 1-D reactive transport equation.•General boundary conditions and smooth initial conditions are considered.•A convenient way is adopted to control and adjust the convergence of series solutions.•Approximate solutions produced by HAM agree well with exact solutions.
The one-dimensional advective-dispersive-reactive transport equation has been widely applied to describe the transportation process of landfill leachate through liners or anti-seepage curtains. However, most existing methods solving this problem are limited to simple initial conditions. In order to eliminate these limitations, homotopy analysis method (HAM) is implemented to solve the contaminant transport model in this paper. Applying auxiliary linear and nonlinear operator, zero order deformation equation is developed to solve contaminant transport problems numerically, with smooth initial conditions and variable source concentration being considered. HAM has been applied to simulate different contamination transport problems in one-dimensional space reported in literature. Good agreement between HAM solutions and analytical solutions has been achieved for all cases considered, demonstrating the feasibility of HAM to solve the contaminant transport model with more general, smooth initial conditions. The one-dimensional advective-dispersive-reactive transport equation has been widely applied to describe the transportation process of landfill leachate through liners or anti-seepage curtains. However, most existing methods solving this problem are limited to simple initial conditions. In order to eliminate these limitations, homotopy analysis method (HAM) is implemented to solve the contaminant transport model in this paper. Applying auxiliary linear and nonlinear operator, zero order deformation equation is developed to solve contaminant transport problems numerically, with smooth initial conditions and variable source concentration being considered. HAM has been applied to simulate different contamination transport problems in one-dimensional space reported in literature. Good agreement between HAM solutions and analytical solutions has been achieved for all cases considered, demonstrating the feasibility of HAM to solve the contaminant transport model with more general, smooth initial conditions. |
| Author | Fang, Dongfang Yu, Xiaoniu Yu, Chuang Wang, Hui Ma, Jianjun Cai, Xiaoqing |
| Author_xml | – sequence: 1 givenname: Chuang surname: Yu fullname: Yu, Chuang organization: College of Architecture and Civil Engineering, Wenzhou University, Wenzhou 325035, China – sequence: 2 givenname: Hui surname: Wang fullname: Wang, Hui organization: College of Architecture and Civil Engineering, Wenzhou University, Wenzhou 325035, China – sequence: 3 givenname: Dongfang surname: Fang fullname: Fang, Dongfang organization: College of Architecture and Civil Engineering, Wenzhou University, Wenzhou 325035, China – sequence: 4 givenname: Jianjun orcidid: 0000-0002-2885-5620 surname: Ma fullname: Ma, Jianjun email: jianjun2004ma@gmail.com organization: School of Civil Engineering, Sun Yat-Sen University, Guangzhou 510006, China – sequence: 5 givenname: Xiaoqing surname: Cai fullname: Cai, Xiaoqing organization: College of Architecture and Civil Engineering, Wenzhou University, Wenzhou 325035, China – sequence: 6 givenname: Xiaoniu surname: Yu fullname: Yu, Xiaoniu organization: College of Architecture and Civil Engineering, Wenzhou University, Wenzhou 325035, China |
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| Snippet | •HAM has been applied to solve 1-D reactive transport equation.•General boundary conditions and smooth initial conditions are considered.•A convenient way is... The one-dimensional advective-dispersive-reactive transport equation has been widely applied to describe the transportation process of landfill leachate... |
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| SubjectTerms | Contaminant deformation equations Homotopy analysis method hydrology Initial condition landfill leachates Transport transportation |
| Title | Semi-analytical solution to one-dimensional advective-dispersive-reactive transport equation using homotopy analysis method |
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