Hi Emanuele, The fact that the terms in the brackets are third order changes things. The terms in the brackets will need to be convection terms. I can help you more with this in a few weeks. In the meantime can you provide the boundary conditions and possible parameter values as well. How the equations are discretized will depend on the various signs of the terms. Also, possible values for phi (e.g. should it always remain positive or between 0 and 1).
Cheers, Daniel On Thu, Oct 21, 2021 at 10:19 AM Emanuele Di Palma <[email protected]> wrote: > > Dear Daniel, > thanks a lot for your answer; > > First of all I'm clarifying that the terms in bracket are third order; > following your suggestions I tried to modify the equation in two ways as > reported in the attached file with the preliminary fipy commands; > it's the first time that I'm using fipy, please, let me know if the commands > I used make sens and I can go ahead. > > Thanks a lot for your help. > > Best Regards, > Emanuele > > > > Il giorno mar 19 ott 2021 alle ore 19:11 Daniel Wheeler > <[email protected]> ha scritto: >> >> Hi Emanuele, >> >> I think this equation is tractable in FiPy with a few tricks. >> Substituting a single variable for the first derivative in time will >> give you two coupled equations. I'm assuming the terms in brackets >> are fourth order terms (can you clarify that). You can also split out >> the second order derivative of phi into another equation resulting in >> three equations that can be coupled. The main equation will need a >> diffusion term with an anisotropic coefficient. The coefficient will >> have a diagonal of 0 and phi on the off diagonal. So to be clear here >> are the three things you need to do >> >> - Substitute out the second order time derivative >> - Substitute out \nabla^2 \phi >> - Use an anisotropic diffusion coefficient in the main equation >> >> These examples are the best examples to get started. >> >> - >> https://www.ctcms.nist.gov/fipy/examples/diffusion/generated/examples.diffusion.coupled.html >> >> - >> https://www.ctcms.nist.gov/fipy/examples/diffusion/generated/examples.diffusion.nthOrder.input4thOrder1D.html >> >> - >> https://www.ctcms.nist.gov/fipy/examples/diffusion/generated/examples.diffusion.anisotropy.html >> >> - >> https://www.ctcms.nist.gov/fipy/examples/phase/generated/examples.phase.anisotropy.html >> >> - >> https://www.ctcms.nist.gov/fipy/examples/phase/generated/examples.phase.polyxtalCoupled.html >> >> - >> https://www.ctcms.nist.gov/fipy/examples/cahnHilliard/generated/examples.cahnHilliard.mesh2DCoupled.html >> >> I hope that helps. >> >> On Tue, Oct 19, 2021 at 10:47 AM Emanuele Di Palma >> <[email protected]> wrote: >> > >> > Daer all, >> > I'd like to solve with FiPy the PDE equation reported in the attached file; >> > I went through the manual and the examples without to find any solution. >> > Please, let me know if it's possible and eventually addressing toward some >> > useful example. >> > >> > Thanks for your attention. >> > >> > Best regards >> > Emanuele Di Palma >> > >> > -- >> > To unsubscribe from this group, send email to >> > [email protected] >> > >> > View this message at https://list.nist.gov/fipy >> > --- >> > To unsubscribe from this group and stop receiving emails from it, send an >> > email to [email protected]. >> >> >> >> -- >> Daniel Wheeler -- Daniel Wheeler -- To unsubscribe from this group, send email to [email protected] View this message at https://list.nist.gov/fipy --- To unsubscribe from this group and stop receiving emails from it, send an email to [email protected].
