Penn station, sukho Thai ?? Sent from my iPhone
On Apr 11, 2013, at 1:09 PM, "Raymond Smith" <[email protected]> wrote: > Hi, > > I'm trying to model a system of a reaction occurring over a 2D particle with > no diffusion in the particle and a reaction rate that depends both on the > concentrations and the electrostatic potential in the particle -- essentially > a non-linear Allen-Cahn model. In this particular case, I'm trying to > describe ions intercalating into a phase separating, low in-plane diffusivity > solid. The basic governing equation looks like > > TransientTerm(var=c) == f(c, Laplacian(c), phi) > > where f(c, Laplacian(c), phi) is some non-linear function of c > (concentration), its second spatial derivatives, and the electrostatic > potential in the solid, phi. The function, f, leads to phase separation in > the particle. > > I'm attempting to model the case of a constant overall current (dis)charge. > Because there is phase separation, and the reaction rate depends on the > concentration in the surface I'm modeling, there is inhomogeneity in the > reaction rate over the 2D surface. However, I'd like the total rate > integrated over the surface to be constant, achieved by varying phi (assumed > to be constant over the surface). > > As of now, I'm doing this with a relatively naive approach of using > scipy.optimize.fsolve at each time step to find the value of the potential, > phi, which leads to the surface integral of dc/dt over the surface being the > desired value. This seems to work reasonably well, but the solvers are > implicit and that seems more like an explicit way to maintain the constraint. > I was wondering if there's a smoother way to incorporate this sort of > integral constraint. I worry that it would actually make the system a DAE, > and I'm not sure (a) if FiPy's integrators are designed to handle that and > (b) how to interact with them if they are. > > Thanks, > Ray > _______________________________________________ > fipy mailing list > [email protected] > http://www.ctcms.nist.gov/fipy > [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ] This message and any attachments are intended for the individual or entity named above. If you are not the intended recipient, please do not forward, copy, print, use or disclose this communication to others; also please notify the sender by replying to this message, and then delete it from your system. The Timken Company / The Timken Corporation _______________________________________________ fipy mailing list [email protected] http://www.ctcms.nist.gov/fipy [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ]
