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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 |
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 23:02, 3 May 2023 | | 1,331 × 376 (24 KB) | SergJim | I changed u for the y-axis and x for the x-axis to match the nomenclature in the "Upwind scheme" wiki page. |
| 22:49, 3 May 2023 |  | 1,331 × 376 (27 KB) | SergJim | I changed the "Cr" symbol to be c and removed "Cmax" to match the "Upwind" wiki page nomenclature. | |
| 22:31, 3 May 2023 |  | 1,331 × 376 (29 KB) | SergJim | I changed the "Cr" symbol to be C and added "Cmax" to match the "Courant–Friedrichs–Lewy condition" nomenclature. | |
| 22:49, 9 March 2023 |  | 958 × 266 (16 KB) | SergJim | Uploaded own work with UploadWizard |
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