A finite difference method formulation based on the time integral domain for the solution of Transient diffusion-advection problem
This paper is concerned with the development of a formulation of the Finite Difference Method, in the solution of the transient diffusion-advection equation. In this approach, a weighting function with respect to time is used in the fundamental differential equation. By assuming a linear variation...
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| Format: | Article |
| Language: | English |
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Universidade Federal de Viçosa (UFV)
2022-06-01
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| Series: | The Journal of Engineering and Exact Sciences |
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| Online Access: | https://periodicos.ufv.br/jcec/article/view/14081 |
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| author | Marcelo Franco de Oliveira Daniele Cristina Thoaldo Rodrigo Dias |
| author_facet | Marcelo Franco de Oliveira Daniele Cristina Thoaldo Rodrigo Dias |
| author_sort | Marcelo Franco de Oliveira |
| collection | DOAJ |
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This paper is concerned with the development of a formulation of the Finite Difference Method, in the solution of the transient diffusion-advection equation. In this approach, a weighting function with respect to time is used in the fundamental differential equation. By assuming a linear variation in some time interval, a time integration is performed. This integration reduces the order of time derivative in the basic equation and the initial conditions can be taken into account directly in consequence. Three pollutant transport problems are presented in order to verify the stability and accuracy of the proposed approach. The results for this approach are compared with the Boundary Element Methods results. The comparisons of numerical results show a good agreement between the furnished results for the proposed approach and the boundary element method results assumed here as reference results. By analyzing the results one can conclude that the formulation presented in this paper is capable of producing accurate results for the problem.
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| format | Article |
| id | doaj-art-50f2228882c94550b47f914d2fefc58d |
| institution | Kabale University |
| issn | 2527-1075 |
| language | English |
| publishDate | 2022-06-01 |
| publisher | Universidade Federal de Viçosa (UFV) |
| record_format | Article |
| series | The Journal of Engineering and Exact Sciences |
| spelling | doaj-art-50f2228882c94550b47f914d2fefc58d2025-02-02T19:56:16ZengUniversidade Federal de Viçosa (UFV)The Journal of Engineering and Exact Sciences2527-10752022-06-018510.18540/jcecvl8iss5pp14081-01iA finite difference method formulation based on the time integral domain for the solution of Transient diffusion-advection problemMarcelo Franco de Oliveira0Daniele Cristina Thoaldo1Rodrigo Dias2Federal University of ParanáTuiuti University of ParanáTuiuti University of Paraná / Federal University of Paraná This paper is concerned with the development of a formulation of the Finite Difference Method, in the solution of the transient diffusion-advection equation. In this approach, a weighting function with respect to time is used in the fundamental differential equation. By assuming a linear variation in some time interval, a time integration is performed. This integration reduces the order of time derivative in the basic equation and the initial conditions can be taken into account directly in consequence. Three pollutant transport problems are presented in order to verify the stability and accuracy of the proposed approach. The results for this approach are compared with the Boundary Element Methods results. The comparisons of numerical results show a good agreement between the furnished results for the proposed approach and the boundary element method results assumed here as reference results. By analyzing the results one can conclude that the formulation presented in this paper is capable of producing accurate results for the problem. https://periodicos.ufv.br/jcec/article/view/14081numerical approach. finite difference method, diffusion-advection. pollutant dispersion. |
| spellingShingle | Marcelo Franco de Oliveira Daniele Cristina Thoaldo Rodrigo Dias A finite difference method formulation based on the time integral domain for the solution of Transient diffusion-advection problem The Journal of Engineering and Exact Sciences numerical approach. finite difference method, diffusion-advection. pollutant dispersion. |
| title | A finite difference method formulation based on the time integral domain for the solution of Transient diffusion-advection problem |
| title_full | A finite difference method formulation based on the time integral domain for the solution of Transient diffusion-advection problem |
| title_fullStr | A finite difference method formulation based on the time integral domain for the solution of Transient diffusion-advection problem |
| title_full_unstemmed | A finite difference method formulation based on the time integral domain for the solution of Transient diffusion-advection problem |
| title_short | A finite difference method formulation based on the time integral domain for the solution of Transient diffusion-advection problem |
| title_sort | finite difference method formulation based on the time integral domain for the solution of transient diffusion advection problem |
| topic | numerical approach. finite difference method, diffusion-advection. pollutant dispersion. |
| url | https://periodicos.ufv.br/jcec/article/view/14081 |
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