A survey of numerical schemes for transportation equation
The convection-diffusion equation is a fundamental equation that exists widely. The convection-diffusion equation consists of two processes: diffusion and convection. The convection-diffusion equation can also be called drift-diffusion equaintion. The convection – diffusion equation mainly character...
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| Format: | Article |
| Language: | English |
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EDP Sciences
2021-01-01
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| Series: | E3S Web of Conferences |
| Online Access: | https://www.e3s-conferences.org/articles/e3sconf/pdf/2021/84/e3sconf_msetee2021_01020.pdf |
| _version_ | 1819239603294437376 |
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| author | Yu Simin |
| author_facet | Yu Simin |
| author_sort | Yu Simin |
| collection | DOAJ |
| description | The convection-diffusion equation is a fundamental equation that exists widely. The convection-diffusion equation consists of two processes: diffusion and convection. The convection-diffusion equation can also be called drift-diffusion equaintion. The convection – diffusion equation mainly characterizes natural phenomenon in which physical particles, energy are transferred in a system. The well-known linear transport equation is also one kind of convection-diffusion equation. The transport equation can describe the transport of a scalar field such as material feature, chemical reaction or temperature in an incompressible flow. In this paper, we discuss the famous numerical scheme, Lax-Friedrichs method, for the linear transport equation. The important ingredient of the design of the Lax-Friedrichs Method, namely the choice of the numerical fluxes will be discussed in detail. We give a detailed proof of the L1 stability of the Lax-Friedrichs scheme for the linear transport equation. We also address issues related to the implementation of this numerical scheme. |
| first_indexed | 2024-12-23T13:54:45Z |
| format | Article |
| id | doaj.art-4056b5ba0a3a42379738ac0149ef6aec |
| institution | Directory Open Access Journal |
| issn | 2267-1242 |
| language | English |
| last_indexed | 2024-12-23T13:54:45Z |
| publishDate | 2021-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | E3S Web of Conferences |
| spelling | doaj.art-4056b5ba0a3a42379738ac0149ef6aec2022-12-21T17:44:29ZengEDP SciencesE3S Web of Conferences2267-12422021-01-013080102010.1051/e3sconf/202130801020e3sconf_msetee2021_01020A survey of numerical schemes for transportation equationYu Simin0Sanyang Road Sanyang Jingchen Community, WuHan UniversityThe convection-diffusion equation is a fundamental equation that exists widely. The convection-diffusion equation consists of two processes: diffusion and convection. The convection-diffusion equation can also be called drift-diffusion equaintion. The convection – diffusion equation mainly characterizes natural phenomenon in which physical particles, energy are transferred in a system. The well-known linear transport equation is also one kind of convection-diffusion equation. The transport equation can describe the transport of a scalar field such as material feature, chemical reaction or temperature in an incompressible flow. In this paper, we discuss the famous numerical scheme, Lax-Friedrichs method, for the linear transport equation. The important ingredient of the design of the Lax-Friedrichs Method, namely the choice of the numerical fluxes will be discussed in detail. We give a detailed proof of the L1 stability of the Lax-Friedrichs scheme for the linear transport equation. We also address issues related to the implementation of this numerical scheme.https://www.e3s-conferences.org/articles/e3sconf/pdf/2021/84/e3sconf_msetee2021_01020.pdf |
| spellingShingle | Yu Simin A survey of numerical schemes for transportation equation E3S Web of Conferences |
| title | A survey of numerical schemes for transportation equation |
| title_full | A survey of numerical schemes for transportation equation |
| title_fullStr | A survey of numerical schemes for transportation equation |
| title_full_unstemmed | A survey of numerical schemes for transportation equation |
| title_short | A survey of numerical schemes for transportation equation |
| title_sort | survey of numerical schemes for transportation equation |
| url | https://www.e3s-conferences.org/articles/e3sconf/pdf/2021/84/e3sconf_msetee2021_01020.pdf |
| work_keys_str_mv | AT yusimin asurveyofnumericalschemesfortransportationequation AT yusimin surveyofnumericalschemesfortransportationequation |