| Author | Message | ||||||
     Wijb Sommer (wijb) Member Username: wijb Post Number: 5 Registered: 12-2007 |
Dear Mr. Nelson, I am working on a time dependent advection-diffusion problem. Because it is non-linear it is difficult to solve. The time step is cut into too small parts (would take a month to solve it). From the history plot from a successful run can be seen that the mass concentration gradient sometimes changes rapidly in time. I think it would be good to damp this. I tried to replace dt(w)... by dt(w)-eps*del2(w)... (eps=1) this gave strange (incorrect) results. Attached are the program, files for initial conditions and a pg5 file from the successful run. The purpose is to increase 'poresizefactor' to 15, but than the timestep problem increases. Increasing diffusion is not an option, because this is the subject of interest (density dependent lateral dispersion/diffusion). I very much hope you can help me. Kind regards, Wijb Sommer
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| Wijb Sommer (wijb) Member Username: wijb Post Number: 6 Registered: 12-2007 |
Actually i realize now that this extra diffusion term "-eps*del2(w) is exactly the same as the diffusion term which is already in the pde for streamfunction psi [-1/pel*dyy(w)-1/pet*dxx(w)]. choosing eps=0.0001 would double the diffusion term, since for my case 1/pel=1/pet=0.0001. Because this diffusion process is the subject of detailed modelling, adding an extra diffusion term makes comparison impossible. Is it not possible to smooth the signal over time? So that changes in mass fraction (w) (gradient) don't happen abruptly. Or have an extra diffusion term which disappears after some time. | ||||||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1130 Registered: 06-2003 |
I have two observations on this script: 1) Your W equation is initial-value, while your Psi equation is an equilibrium boundary-value equation. The fact that Psi has no hysteresis but equilibrates instantaneously removes it from timestep control and allows oscillation. I suggest that you restore whatever time derivative term would have been in the full description of the psi system, or, if there is none, to introduce a pseudo-time behavior of Psi. Simply add the term tau*dt(psi) to the right-hand side of the Psi equation. Here tau is the relaxation time (reciprocal coupling strength) over which Psi reacts to its environment. This adds a memory term to Psi, which tends to damp oscillations. 2) The noise in dx(w) at the right end seems to me to be a symptom of an inconsistency between the boundary conditions and PDE solution. If the two are in conflict, it can cause this kind of oscillation. From the pictures it seems clear that Psi does not really want to be equal to Y at the sides. You might want to rethink what this means and whether it is appropriate to the system under investigation. What is the physical mechanism that imposes this condition? |
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