A finite Volume Runge-Kutta Ellam Method for the Solution of Advection Diffusion Equations
We develop a finite volume characteristic method for the solution of the advection-diffusion equations which model the contaminant transport through porous medium. This method uses a second order Runge-Kutta approximation for the characteristics within the framework of the Eulerian Lagrangian locali...
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| Format: | Article |
| Language: | English |
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Sultan Qaboos University
2001-12-01
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| Series: | Sultan Qaboos University Journal for Science |
| Subjects: | |
| Online Access: | https://journals.squ.edu.om/index.php/squjs/article/view/269 |
| _version_ | 1818483618173943808 |
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| author | Mohammed Al-Lawatia Robert C. Sharpley Hong Wang |
| author_facet | Mohammed Al-Lawatia Robert C. Sharpley Hong Wang |
| author_sort | Mohammed Al-Lawatia |
| collection | DOAJ |
| description | We develop a finite volume characteristic method for the solution of the advection-diffusion equations which model the contaminant transport through porous medium. This method uses a second order Runge-Kutta approximation for the characteristics within the framework of the Eulerian Lagrangian localized adjoint methods (ELLAM). The derived scheme conserves mass, symmetrizes the governing equations and generates accurate numerical solutions even if large time steps are used. Numerical experiments comparing several competitive methods using a standard test example are presented to illustrate the performance of the method. |
| first_indexed | 2024-12-10T15:44:16Z |
| format | Article |
| id | doaj.art-aae26f47df8f4ad0ae65cacebbabde89 |
| institution | Directory Open Access Journal |
| issn | 1027-524X 2414-536X |
| language | English |
| last_indexed | 2024-12-10T15:44:16Z |
| publishDate | 2001-12-01 |
| publisher | Sultan Qaboos University |
| record_format | Article |
| series | Sultan Qaboos University Journal for Science |
| spelling | doaj.art-aae26f47df8f4ad0ae65cacebbabde892022-12-22T01:43:00ZengSultan Qaboos UniversitySultan Qaboos University Journal for Science1027-524X2414-536X2001-12-0162678310.24200/squjs.vol6iss2pp67-83268A finite Volume Runge-Kutta Ellam Method for the Solution of Advection Diffusion EquationsMohammed Al-Lawatia0Robert C. Sharpley1Hong Wang2Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box 36 Al-Khod 123, Sultanate of Oman.Industrial Mathematics Institute, Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208, USA.Industrial Mathematics Institute, Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208, USA.We develop a finite volume characteristic method for the solution of the advection-diffusion equations which model the contaminant transport through porous medium. This method uses a second order Runge-Kutta approximation for the characteristics within the framework of the Eulerian Lagrangian localized adjoint methods (ELLAM). The derived scheme conserves mass, symmetrizes the governing equations and generates accurate numerical solutions even if large time steps are used. Numerical experiments comparing several competitive methods using a standard test example are presented to illustrate the performance of the method.https://journals.squ.edu.om/index.php/squjs/article/view/269Characteristics methods, Comparison of numerical methods, Eulerian-Lagrangian methods, Numerical solutions of advection-diffusion equations, Runge-Kutta methods. |
| spellingShingle | Mohammed Al-Lawatia Robert C. Sharpley Hong Wang A finite Volume Runge-Kutta Ellam Method for the Solution of Advection Diffusion Equations Sultan Qaboos University Journal for Science Characteristics methods, Comparison of numerical methods, Eulerian-Lagrangian methods, Numerical solutions of advection-diffusion equations, Runge-Kutta methods. |
| title | A finite Volume Runge-Kutta Ellam Method for the Solution of Advection Diffusion Equations |
| title_full | A finite Volume Runge-Kutta Ellam Method for the Solution of Advection Diffusion Equations |
| title_fullStr | A finite Volume Runge-Kutta Ellam Method for the Solution of Advection Diffusion Equations |
| title_full_unstemmed | A finite Volume Runge-Kutta Ellam Method for the Solution of Advection Diffusion Equations |
| title_short | A finite Volume Runge-Kutta Ellam Method for the Solution of Advection Diffusion Equations |
| title_sort | finite volume runge kutta ellam method for the solution of advection diffusion equations |
| topic | Characteristics methods, Comparison of numerical methods, Eulerian-Lagrangian methods, Numerical solutions of advection-diffusion equations, Runge-Kutta methods. |
| url | https://journals.squ.edu.om/index.php/squjs/article/view/269 |
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