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]
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