Hi Emanuele, Sorry for taking so long to respond to this. I used what you did with the first set of equations and rearranged some more to something that I think is tractable in FiPy (unless I messed up, please check). See the attached PDF. If that is correct, then I think that form as written is tractable in FiPy. Every term is either a TransientTerm or a DiffusionTerm (the first equation is just a source on the right hand side, which should probably be explicit). Also, all the equations are transient as written which gives more control over the stability. I would imagine that with smaller alphas that the system is more stable. I would start with a very small alpha and see how stability is impacted as you move towards the physical value of alpha (make sure the equations solve with alpha=0 to start).
In your attached PDF in the previous email you have coefficients multiplying diffusion terms. That does not work in FiPy. Everything needs to be inside the operator. Hence how I wrote the equations. Try and implement this in FiPy and the I'll take another look if you can't get things working. Cheers, Daniel On Fri, Oct 22, 2021 at 4:11 AM Emanuele Di Palma <emanueledipalm...@gmail.com> wrote: > > Hi Daniel, > > thanks a lot for your message. > > Regarding the coefficients we have \alpha=1 and \gamma=0.0188, Neumann type > must be the boundary condition. > \alpha represents the normalized scalar potential and it can oscillate from > negative to positive values, the initial condition could be: > \alpha(t=0)=\phi_0+random_perturbation wiht \phi_0 around 10^-2 and > 0<D_t(\phi)(0)<<1. > > Thanks a lot for your availability. > > Best Regards, > Emanuele > > > Il giorno gio 21 ott 2021 alle ore 19:49 Daniel Wheeler > <daniel.wheel...@gmail.com> ha scritto: >> >> 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 >> <emanueledipalm...@gmail.com> 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 >> > <daniel.wheel...@gmail.com> 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 >> >> <emanueledipalm...@gmail.com> 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 >> >> > fipy+unsubscr...@list.nist.gov >> >> > >> >> > View this message at https://list.nist.gov/fipy >> >> > --- >> >> > To unsubscribe from this group and stop receiving emails from it, send >> >> > an email to fipy+unsubscr...@list.nist.gov. >> >> >> >> >> >> >> >> -- >> >> Daniel Wheeler >> >> >> >> -- >> Daniel Wheeler -- Daniel Wheeler -- To unsubscribe from this group, send email to fipy+unsubscr...@list.nist.gov View this message at https://list.nist.gov/fipy --- To unsubscribe from this group and stop receiving emails from it, send an email to fipy+unsubscr...@list.nist.gov.
CodeCogsEqn.pdf
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