Timeline for Nondimensionalization of a multi-component chemical diffusion equation
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 17, 2022 at 22:21 | vote | accept | Iddingsite | ||
| Feb 16, 2022 at 21:16 | comment | added | Iddingsite | Thx for your contribution. First, to clarify, my matrix $\textbf{D}$ is not symmetric and is changing through time and space. I see how I can compute the eigenvalues numerically, and hence the different time scales. But as the equations are coupled, is that not a problem if they don't have the same dimensionless time? | |
| Feb 16, 2022 at 19:16 | answer | added | Wolfgang Bangerth | timeline score: 3 | |
| Feb 16, 2022 at 18:41 | comment | added | Daniel Shapero | I think it's worth seeing if you can compute the eigenvalue decomposition of the diffusion matrix $D$, which should be symmetric. The eigenvalues will give you three diffusion coefficients, from which you can compute the corresponding characteristic time scales, taking the diameter of the domain as a length. Those time scales might be very different from each other. If you can't compute the eigendecomposition analytically, you might nonetheless be able to get something quantitative through the Gerschgorin circle theorem. | |
| Feb 16, 2022 at 18:27 | comment | added | Iddingsite | I've corrected the equations. Thx for pointing this out! | |
| Feb 16, 2022 at 18:27 | history | edited | Iddingsite | CC BY-SA 4.0 |
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| Feb 16, 2022 at 17:36 | comment | added | Iddingsite | You are right, my equations are wrong. I will modify my post asap! | |
| Feb 16, 2022 at 16:31 | comment | added | Wolfgang Bangerth | Separately, I don't understand the equations. How would the change in concentration for Mg depend on the gradient of the concentration of Fe? Are you consider element transmutation? | |
| Feb 16, 2022 at 16:30 | comment | added | Wolfgang Bangerth | You might want to fix the spelled out 2x2 system to make sure it matches the original matrix system. I suspect that you need $C_{Fe}$ to show up in the first equation, and $C_{Mg}$ to show up in the second. | |
| Feb 16, 2022 at 15:06 | history | asked | Iddingsite | CC BY-SA 4.0 |