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 > -- 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.
