File:First Order Upwind Scheme Stability.png
Jump to navigation
Jump to search
Size of this preview: 800 × 226 pixels. Other resolutions: 320 × 90 pixels | 1,331 × 376 pixels.
Original file (1,331 × 376 pixels, file size: 24 KB, MIME type: image/png)
Summary
| Description |
English: When the first-order upwind scheme is applied to the one-dimensional time-dependent advection equation, the courant number is formed as an indicator of the scheme's stability. The scheme is stable as long as the courant number is less than or equal to one. When the courant number is one, the exact solution is formed. In the figure above, the exact solution is a square pulse with no diffusion. If the courant number is less than one, than numerical diffusion will occur which is not the actual diffusion that the solution experiences, shown with in the figure above where the two graphs on the left have some spreading, when the actual solution is a square pulse. When the courant number is larger than one, the scheme will begin to create large oscillations and grow unstable, as seen with the graph on the far right. |
| Date | |
| Source | Own work |
| Author | SergJim |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
|
This media file is uncategorized.
Please help improve this media file by adding it to one or more categories, so it may be associated with related media files (how?), and so that it can be more easily found.
Please notify the uploader with {{subst:Please link images|File:First Order Upwind Scheme Stability.png}} ~~~~ |
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 00:02, 4 May 2023 | | 1,331 × 376 (24 KB) | wikimediacommons>SergJim | I changed u for the y-axis and x for the x-axis to match the nomenclature in the "Upwind scheme" wiki page. |
File usage
The following page uses this file:
