Hi, Ian. Some thoughts. Are you able to give us any more detail about your PDE? For example, the form/meaning of the things in the source term on the right hand side? Presumably the flux is defined by \sigma \nabla \phi If so, then not specifying any boundary conditions would lead to no-flux conditions because FiPy defaults to assuming zero-gradients for field variables on the boundary. However, you could do it explicitly with something like phi.faceGrad.constrain([0.], mesh.exteriorFaces)
However, the form of the source is important here because if the integral of the source is non-zero, then there is no steady solution. If the integral _is_ zero and the source is not a function of \phi, then the system admits an infinite family of solutions, all shifted by a constant. There's some discussion of this issue in the 1D diffusion example: http://www.ctcms.nist.gov/fipy/examples/diffusion/generated/examples.diffusion.mesh1D.html#module-examples.diffusion.mesh1D Search for "Fully implicit solutions are not without their pitfalls" Best, Ray On Thu, May 26, 2016 at 6:30 AM, Campbell, Ian <i.campbel...@imperial.ac.uk> wrote: > Dear All, > > > > Thanks for the great work on FiPy so far. > > > > We have a 2nd order elliptic PDE* defined in the domain (0, 1). At each > boundary, we have a no-flux boundary condition. > > > > We have tried to represent this in FiPy, but specifying such conditions > results only in incorrect results with large error. We have searched this > page (below) in depth but can’t see which function call is appropriate, if > any. > > > > http://www.ctcms.nist.gov/fipy/fipy/generated/fipy.boundaryConditions.html > > > > Do you have a recommendation for how we may implement two no-flux boundary > conditions on our PDE? > > > > Best regards, > > > > - Ian > > > > * $$\nabla.(\sigma_{eff} \nabla \bar{\phi}_s) = a_s F \bar{j}$$ > > > > 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: i.campbel...@imperial.ac.uk > > > > _______________________________________________ > fipy mailing list > fipy@nist.gov > http://www.ctcms.nist.gov/fipy > [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ] > >
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