Ray - Thanks for your very complete and very correct answers to Dario.
If you wouldn't mind transcribing your answer to Dario's question on StackOverflow, I'd be happy to up-vote it. In answer to *your* questions: > On Apr 3, 2016, at 11:09 AM, Raymond Smith <[email protected]> wrote: > > Actually, I'm not sure how FiPy treats the steady-state initial guess for > Laplace's equation with no flux boundary conditions like yours here. The > governing equation + BC's without an initial condition admits any uniform > profile as a solution. > I'm still unsure about the treatment of the initial phi values in this sense > as mentioned above. > However, the direct-to-steady approach merits a few words of caution. First, > there isn't really a good numerical way of directly computing steady state > solutions for general systems. Often, your best bet is actually to solve the > transient equation by time stepping from some initial condition until you > reach steady state, as that's actually probably the most robust algorithm for > solving for steady state profiles. The situation is as you expect. We talk about this toward the end of http://www.ctcms.nist.gov/fipy/examples/diffusion/generated/examples.diffusion.mesh1D.html (search for "Fully implicit solutions are not without their pitfalls"). Basically, a steady-state diffusive problem will "lose" its initial condition and should instead be solved by relaxation. The timestep can be made very large; there just needs to be a TransientTerm. Note, also, that it's not necessary to constrain the gradient to zero to get no-flux. FiPy is a cell-centered finite volume code, so no-flux is the natural boundary condition if nothing else is specified. - Jon _______________________________________________ fipy mailing list [email protected] http://www.ctcms.nist.gov/fipy [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ]
