| Issue |
E3S Web Conf.
Volume 308, 2021
2021 6th International Conference on Materials Science, Energy Technology and Environmental Engineering (MSETEE 2021)
|
|
|---|---|---|
| Article Number | 01020 | |
| Number of page(s) | 7 | |
| Section | Energy Resource Development and Energy Saving Technology | |
| DOI | https://doi.org/10.1051/e3sconf/202130801020 | |
| Published online | 27 September 2021 | |
A survey of numerical schemes for transportation equation
Sanyang Road Sanyang Jingchen Community, WuHan University, WuHan, Hubei, 430010, China
* Corresponding author’s e-mail: 2016300030055@whu.edu.cn
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.
© The Authors, published by EDP Sciences, 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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