A finite Volume Runge-Kutta Ellam Method for the Solution of Advection Diffusion Equations

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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Bibliographic Details
Main Authors: Mohammed Al-Lawatia, Robert C. Sharpley, Hong Wang
Format: Article
Language:English
Published: Sultan Qaboos University 2001-12-01
Series:Sultan Qaboos University Journal for Science
Subjects:
Characteristics methods, Comparison of numerical methods, Eulerian-Lagrangian methods, Numerical solutions of advection-diffusion equations, Runge-Kutta methods.
Online Access:https://journals.squ.edu.om/index.php/squjs/article/view/269
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spelling doaj-aae26f47df8f4ad0ae65cacebbabde892020-11-24T22:35:06ZengSultan 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.
collection DOAJ
language English
format Article
sources DOAJ
author Mohammed Al-Lawatia
Robert C. Sharpley
Hong Wang
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.
author_facet Mohammed Al-Lawatia
Robert C. Sharpley
Hong Wang
author_sort Mohammed Al-Lawatia
title 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_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_sort finite volume runge-kutta ellam method for the solution of advection diffusion equations
publisher Sultan Qaboos University
series Sultan Qaboos University Journal for Science
issn 1027-524X
2414-536X
publishDate 2001-12-01
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.
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
work_keys_str_mv AT mohammedallawatia afinitevolumerungekuttaellammethodforthesolutionofadvectiondiffusionequations
AT robertcsharpley afinitevolumerungekuttaellammethodforthesolutionofadvectiondiffusionequations
AT hongwang afinitevolumerungekuttaellammethodforthesolutionofadvectiondiffusionequations
AT mohammedallawatia finitevolumerungekuttaellammethodforthesolutionofadvectiondiffusionequations
AT robertcsharpley finitevolumerungekuttaellammethodforthesolutionofadvectiondiffusionequations
AT hongwang finitevolumerungekuttaellammethodforthesolutionofadvectiondiffusionequations
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