Timeline for Numerical solution of an advection equation, $\frac{\partial P}{\partial t}+\frac{\partial}{\partial x}\left(P^{5/3}\right)=0$, with finite volume
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 27, 2023 at 15:58 | vote | accept | Sayan | ||
| Jan 24, 2023 at 22:43 | answer | added | Rigel | timeline score: 4 | |
| Jan 22, 2023 at 6:33 | comment | added | Sayan | I am trying with a single global dt only. But the concern is how to compute it from the CFL condition. As I am doing a finite volume discretization, it demands the velocity to be known at the cell boundary or $5/3P_{i+1/2}^{2/3}$. So how should I compute that ? | |
| Jan 21, 2023 at 21:37 | comment | added | helloworld922 | you should have a single dt for the entire domain, try using the largest value in the entire domain of $a \approx \partial (P^{5/3})/\partial P = 5/3 P^{2/3} $ for that timestep. | |
| Jan 21, 2023 at 16:56 | comment | added | Sayan | For linear problem, it is giving the right output. This is leading me to think if the calculation for "dt" that I am performing is correct or not. I was calculating dt in the following manner,$$ dt=\mathcal{C}dx/P_{i}^{2/3}$$. For the right calculation instead of $P_{i}^{2/3}$ one needs to take $P_{i+1/2}^{2/3}$ but I do not know what is the value of $P_{i+1/2}$. Could this be the problem ? | |
| Jan 20, 2023 at 18:04 | comment | added | Wolfgang Bangerth | Then have you tried to debug your code? Maybe by solving a linear problem at first? | |
| Jan 20, 2023 at 10:47 | comment | added | Sayan | Yes it is. I wrote it for completeness. The flux will only going to take the left value. | |
| Jan 19, 2023 at 20:39 | comment | added | Wolfgang Bangerth | The equation clearly only makes sense if $P\ge 0$. But then the question remains under what circumstances you consider $P^{2/3}<0$? If $P\ge 0$, isn't $P^{2/3}$ always greater or equal to zero? | |
| S Jan 19, 2023 at 18:24 | review | First questions | |||
| Jan 20, 2023 at 12:32 | |||||
| S Jan 19, 2023 at 18:24 | history | asked | Sayan | CC BY-SA 4.0 |