Timeline for How can I check mass conservation when solving the advection equation using an upwind scheme?
Current License: CC BY-SA 4.0
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| Jul 13, 2022 at 4:23 | history | edited | nicholaswogan | CC BY-SA 4.0 |
added 24 characters in body
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| Jul 6, 2022 at 10:56 | comment | added | EMP | They really only become the same approximation under very simplified circumstances, once you get into the realm of nonlinear multidimensional PDEs this almost never happens, and talking about a venn diagram between them is more confusing than it is illuminating. | |
| Jul 6, 2022 at 8:26 | comment | added | IPribec | Philip Roe left a great answer to this subquestion in scicomp.stackexchange.com/a/30277/37438 | |
| Jul 6, 2022 at 6:47 | comment | added | nicholaswogan | Subset isn't right. But it seems like there is a Venn diagram between FV and FD. You can start with the strong form with FD, or the weak form and apply FV, and end up with the same approximation. | |
| Jul 6, 2022 at 0:30 | comment | added | EMP | That is not correct. FD is solving the strong form, FV and FEM the weak form. | |
| Jul 5, 2022 at 22:00 | vote | accept | nicholaswogan | ||
| Jul 5, 2022 at 22:00 | comment | added | nicholaswogan | My understanding is that FV methods are the subset of FD methods that are conserving. | |
| Jul 5, 2022 at 17:30 | comment | added | EMP | Non FV schemes still are conservative. You just need to use a conservative method. For example the edge-based discretization which is commonly referred to as node-centered finite volume is actually a finite difference scheme. It maintains conservation because it still uses a flux balance. There are conservative FD, FV, and FE discretizations. | |
| Jul 5, 2022 at 16:31 | history | answered | nicholaswogan | CC BY-SA 4.0 |