Timeline for Nondimensionalization of a multi-component chemical diffusion equation
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 17, 2022 at 22:21 | vote | accept | Iddingsite | ||
| Feb 17, 2022 at 22:21 | comment | added | Iddingsite | Alright, thx for your patience! I have everything I need to make this work. Thx for your help! | |
| Feb 17, 2022 at 22:13 | comment | added | Wolfgang Bangerth | You need to pick one time scale. For a 3x3 matrix, you really only get three values (based on the three eigenvalues of the matrix), and consequently you have to decide which of the three time scales that correspond to these eigenvalues is most relevant to you. You can take some kind of average, or the largest, or the smaller -- all are defensible choices. | |
| Feb 17, 2022 at 14:56 | comment | added | Iddingsite | I see. I have 1 last question and then I will consider this question solved. How can I solve my system if I have 9 different $\tau^*$ for each component of D? Is that not a problem? Or should I fix $\tau^*$ for 1 value of the matrix $ \textbf{D}$? | |
| Feb 17, 2022 at 5:12 | comment | added | Wolfgang Bangerth | Yes. You will obtain a scaled version of $D$, but it will not be the identity matrix. | |
| Feb 16, 2022 at 21:12 | comment | added | Iddingsite | Thx for the answer! Diagonalizing the system is clearly not possible in my case, but that is definitely an elegant way to do it for simpler cases. Concerning the eigenvalues, let's say I take the mean of the mean for the 3 eigenvalues on every point from the initial condition. How can I link it to the nondimensionalization? Should $\textbf{D}^*$ be equal to this? If so, it means that I will obtain different timescale for each component of $\textbf{D}$ right? | |
| Feb 16, 2022 at 19:16 | history | answered | Wolfgang Bangerth | CC BY-SA 4.0 |