Numerical Solutions of Advection Diffusion Equations Using Finite Element Method
n this paper, we have implemented the finite element method for the numerical solution of a boundary and initial value problems, mainly on solving the one and two-dimensional advection-diffusion equation with constant parameters. In doing so, the basic idea is to first rewrite the problem as a vari...
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| Format: | Article |
| Language: | English |
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Hawassa University
2023-04-01
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| Series: | East African Journal of Biophysical and Computational Sciences |
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| Online Access: | https://www.Ajol.Info/index.php/eajbcs/article/view/248706 |
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| author | Kassahun Getnet Mekonen Zerihun Kinfe Birhanu |
| author_facet | Kassahun Getnet Mekonen Zerihun Kinfe Birhanu |
| author_sort | Kassahun Getnet Mekonen |
| collection | DOAJ |
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n this paper, we have implemented the finite element method for the numerical solution of a boundary and initial value problems, mainly on solving the one and two-dimensional advection-diffusion equation with constant parameters. In doing so, the basic idea is to first rewrite the problem as a variational equation, and then seek a solution approximation from the space of continuous piece-wise linear’s. This discretization procedure results in a linear system that can be solved by using a numerical algorithm for systems of these equations. The techniques are based on the finite element approximations using Galerkin’s method in space resulting system of the first order ODE’s and then solving this first order ODE’s using backward Euler descritization in time. For the two-dimensional problems, we use the ODE solver ODE15I to descritize time. The validity of the numerical model is verified using different
test examples. The computed results showed that the use of the current method is very applicable for the solution of the advection-diffusion equation.
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| format | Article |
| id | doaj-art-55730d54ca534de7bcffb621c806cb3e |
| institution | Kabale University |
| issn | 2789-360X 2789-3618 |
| language | English |
| publishDate | 2023-04-01 |
| publisher | Hawassa University |
| record_format | Article |
| series | East African Journal of Biophysical and Computational Sciences |
| spelling | doaj-art-55730d54ca534de7bcffb621c806cb3e2025-02-08T19:51:01ZengHawassa UniversityEast African Journal of Biophysical and Computational Sciences2789-360X2789-36182023-04-0141Numerical Solutions of Advection Diffusion Equations Using Finite Element MethodKassahun Getnet Mekonen0Zerihun Kinfe Birhanu1Department of Mathematics, College of Natural and Computational Sciences, Hawassa University, Hawassa, Ethiopia. Department of Mathematics, College of Natural and Computational Sciences, Hawassa University, Hawassa, Ethiopia. n this paper, we have implemented the finite element method for the numerical solution of a boundary and initial value problems, mainly on solving the one and two-dimensional advection-diffusion equation with constant parameters. In doing so, the basic idea is to first rewrite the problem as a variational equation, and then seek a solution approximation from the space of continuous piece-wise linear’s. This discretization procedure results in a linear system that can be solved by using a numerical algorithm for systems of these equations. The techniques are based on the finite element approximations using Galerkin’s method in space resulting system of the first order ODE’s and then solving this first order ODE’s using backward Euler descritization in time. For the two-dimensional problems, we use the ODE solver ODE15I to descritize time. The validity of the numerical model is verified using different test examples. The computed results showed that the use of the current method is very applicable for the solution of the advection-diffusion equation. https://www.Ajol.Info/index.php/eajbcs/article/view/248706Finite Element Method; Varational Formulation; Numerical integration |
| spellingShingle | Kassahun Getnet Mekonen Zerihun Kinfe Birhanu Numerical Solutions of Advection Diffusion Equations Using Finite Element Method East African Journal of Biophysical and Computational Sciences Finite Element Method; Varational Formulation; Numerical integration |
| title | Numerical Solutions of Advection Diffusion Equations Using Finite Element Method |
| title_full | Numerical Solutions of Advection Diffusion Equations Using Finite Element Method |
| title_fullStr | Numerical Solutions of Advection Diffusion Equations Using Finite Element Method |
| title_full_unstemmed | Numerical Solutions of Advection Diffusion Equations Using Finite Element Method |
| title_short | Numerical Solutions of Advection Diffusion Equations Using Finite Element Method |
| title_sort | numerical solutions of advection diffusion equations using finite element method |
| topic | Finite Element Method; Varational Formulation; Numerical integration |
| url | https://www.Ajol.Info/index.php/eajbcs/article/view/248706 |
| work_keys_str_mv | AT kassahungetnetmekonen numericalsolutionsofadvectiondiffusionequationsusingfiniteelementmethod AT zerihunkinfebirhanu numericalsolutionsofadvectiondiffusionequationsusingfiniteelementmethod |