Q1: You should be able to solve some equations coupled and others uncoupled. You'll need to sweep them all together. Better would be to figure out how to couple them all. I don't recommend doing them uncoupled, I just couldn't quickly get it to work.
Q2: In general, the coupled forms should converge faster. On the other hand, they involve a larger matrix, so they'll take more memory and, sometimes, may not solve at all. As I said in my earlier answer, I think the "waste" of doing the solutions for all three equations over the entire domain is outweighed by being able to make more things implicit and coupled. I recommend you test the memory and speed demands of both approaches, though. > On Jul 21, 2016, at 1:04 PM, Campbell, Ian <[email protected]> > wrote: > > Dear Jonathan, > > Thank you very much for your gist* explanation of how to couple the PDEs > along the upper boundary of a 2D mesh. Your source code is invaluable and has > helped us to get back on track. We have two follow-up questions as a result: > > Question 1: > As an extension of this problem, we’re interested in adding a third PDE > (PDE3) to the system (this PDE is similar in form to a standard > advection-diffusion equation). This third PDE is defined only along the > x-axis at the top of the Cartesian grid, just as with PDE1. A component in > the source term of PDE3 is the cellvariable in PDE1. Furthermore, another > component in the source term of PDE3 exists in the boundary condition of > PDE2. That is to say, PDE1 and PDE3 interact as fully coupled equations along > the x-axis at the top of the mesh. PDE1 and PDE3 in-turn interact with PDE2 > (anisotropic diffusion) along the top of the mesh only. > > Our question is as follows; given that you have proposed the uncoupled method > with repeated sweeping for solving the system of PDE1 and PDE2, does this > preclude us from using the fully-coupled “&” method to couple between PDE1 > and PDE3? Phrased differently, if we use the uncoupled sweeping method for > PDE1 and PDE2, must we continue to use this approach when introducing more > axial-domain PDEs? > > Question 2: > In the FiPy coupled-diffusion example (hyperlink below**), the following > statement is made: "The uncoupled method still works, but it can be > advantageous to solve the two equations simultaneously." Can you please > elaborate on this so that we may better understand what the disadvantages of > using the uncoupled, repeated sweep method may be, relative to coupling using > the “&” operator? Especially given that in our problem, the full-2D > implementation has interactions only at the domain’s top-edge and it seems to > be wasteful of computing resources? > > Sincerely, > > - Ian & Krishna > > * https://gist.github.com/guyer/bb199559c00f6047d466daa18554d83d > ** > http://www.ctcms.nist.gov/fipy/examples/diffusion/generated/examples.diffusion.coupled.html > > > Ian Campbell | PhD Candidate > Electrochemical Science & Engineering Group > Room 506, City & Guilds Building, Imperial College London, SW7 2AZ, United > Kingdom > Phone: +44 (0)7449 815 520 | E-mail: [email protected] > > _______________________________________________ > fipy mailing list > [email protected] > http://www.ctcms.nist.gov/fipy > [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ] _______________________________________________ fipy mailing list [email protected] http://www.ctcms.nist.gov/fipy [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ]
