A Stable and High Accurate Numerical Simulator for Convection-Diffusion Equation
This study presents a simulator to obtain numerical solution of convection-diffusion equation. It includes explicit, fully implicit and semi-implicit time discretization techniques. Although the explicit method is efficient for some simple conduction problems, it needs stability criteria. Otherwise,...
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| Language: | English |
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Çanakkale Onsekiz Mart University
2022-03-01
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| Series: | Journal of Advanced Research in Natural and Applied Sciences |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/1937212 |
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| author | Osman Ünal |
| author_facet | Osman Ünal |
| author_sort | Osman Ünal |
| collection | DOAJ |
| description | This study presents a simulator to obtain numerical solution of convection-diffusion equation. It includes explicit, fully implicit and semi-implicit time discretization techniques. Although the explicit method is efficient for some simple conduction problems, it needs stability criteria. Otherwise, it is unstable especially for high Courant number and large time step size. When using the explicit method, the time step size is chosen with care to get well-posed numerical solution. This requirement sets a serious constraint for the explicit method because choosing small time step size causes the simulation time to become quite long. Even though the implicit method is stable for large time step size and high Courant number, it leads to numerical dispersion like the explicit method. On the other hand, second-order accurate semi-implicit method significantly reduces numerical dispersion. In addition to time discretization techniques, this simulator contains several space discretization methods such as first-order upstream and UMIST (University of Manchester Institute of Science and Technology) techniques. The proposed numerical simulator is suitable for easily using the different combinations of time and space discretization methods. Secondly, this study is to propose the use of semi-implicit time discretization technique with UMIST space discretization method to minimize numerical dispersion and suppress unphysical oscillation. In spite of the fact that the UMIST method suppresses unphysical oscillation, it causes a small and undesired oscillation at flood front for very large Courant number. Third objective of this study is to propose minor modification on the UMIST method to eliminate this unphysical oscillation. |
| format | Article |
| id | doaj-art-6e6acfdf3d7748d3a804b1b99851df68 |
| institution | Kabale University |
| issn | 2757-5195 |
| language | English |
| publishDate | 2022-03-01 |
| publisher | Çanakkale Onsekiz Mart University |
| record_format | Article |
| series | Journal of Advanced Research in Natural and Applied Sciences |
| spelling | doaj-art-6e6acfdf3d7748d3a804b1b99851df682025-02-05T17:58:10ZengÇanakkale Onsekiz Mart UniversityJournal of Advanced Research in Natural and Applied Sciences2757-51952022-03-0181455310.28979/jarnas.985946453A Stable and High Accurate Numerical Simulator for Convection-Diffusion EquationOsman Ünal0https://orcid.org/0000-0003-1101-6561SAKARYA UNIVERSITY OF APPLIED SCIENCESThis study presents a simulator to obtain numerical solution of convection-diffusion equation. It includes explicit, fully implicit and semi-implicit time discretization techniques. Although the explicit method is efficient for some simple conduction problems, it needs stability criteria. Otherwise, it is unstable especially for high Courant number and large time step size. When using the explicit method, the time step size is chosen with care to get well-posed numerical solution. This requirement sets a serious constraint for the explicit method because choosing small time step size causes the simulation time to become quite long. Even though the implicit method is stable for large time step size and high Courant number, it leads to numerical dispersion like the explicit method. On the other hand, second-order accurate semi-implicit method significantly reduces numerical dispersion. In addition to time discretization techniques, this simulator contains several space discretization methods such as first-order upstream and UMIST (University of Manchester Institute of Science and Technology) techniques. The proposed numerical simulator is suitable for easily using the different combinations of time and space discretization methods. Secondly, this study is to propose the use of semi-implicit time discretization technique with UMIST space discretization method to minimize numerical dispersion and suppress unphysical oscillation. In spite of the fact that the UMIST method suppresses unphysical oscillation, it causes a small and undesired oscillation at flood front for very large Courant number. Third objective of this study is to propose minor modification on the UMIST method to eliminate this unphysical oscillation.https://dergipark.org.tr/en/download/article-file/1937212finite difference methodhigh-resolution schemeexplicit methodfully implicit methodsemi-implicit method |
| spellingShingle | Osman Ünal A Stable and High Accurate Numerical Simulator for Convection-Diffusion Equation Journal of Advanced Research in Natural and Applied Sciences finite difference method high-resolution scheme explicit method fully implicit method semi-implicit method |
| title | A Stable and High Accurate Numerical Simulator for Convection-Diffusion Equation |
| title_full | A Stable and High Accurate Numerical Simulator for Convection-Diffusion Equation |
| title_fullStr | A Stable and High Accurate Numerical Simulator for Convection-Diffusion Equation |
| title_full_unstemmed | A Stable and High Accurate Numerical Simulator for Convection-Diffusion Equation |
| title_short | A Stable and High Accurate Numerical Simulator for Convection-Diffusion Equation |
| title_sort | stable and high accurate numerical simulator for convection diffusion equation |
| topic | finite difference method high-resolution scheme explicit method fully implicit method semi-implicit method |
| url | https://dergipark.org.tr/en/download/article-file/1937212 |
| work_keys_str_mv | AT osmanunal astableandhighaccuratenumericalsimulatorforconvectiondiffusionequation AT osmanunal stableandhighaccuratenumericalsimulatorforconvectiondiffusionequation |