Handling integral terms with FiPy

[pavaninguva]

Hi

I was wondering if it is FiPy currently includes any support for PDEs with integral terms e.g. population balance models with integral terms to account for breakage etc (see https://aiche.onlinelibrary.wiley.com/doi/full/10.1002/aic.11484 for a bit more detail). If not, would it be possible to use a scipy function call and supply that result as an explicit source term?

Thanks for the help!

[wd15]

Hi Pavan, I don't think FiPy handles these types of equations very well. They are purely hyperbolic looking at the paper. FiPy also hasn't got any examples with integral terms though I imagine those could be implemented. Regardless, it's not FiPy's strong point. You might want to look into Clawpack as an alternative for high resolution sharp interface tracking solvers. Cheers, Daniel

…

On Fri, Oct 1, 2021 at 1:58 AM Pavan Inguva ***@***.***> wrote: Hi I was wondering if it is FiPy currently includes any support for PDEs with integral terms e.g. population balance models with integral terms to account for breakage etc (see https://aiche.onlinelibrary.wiley.com/doi/full/10.1002/aic.11484 for a bit more detail). If not, would it be possible to use a scipy function call and supply that result as an explicit source term? Thanks for the help! — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#824>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAPFCHAILSZIOS6256OXXRDUEVEX7ANCNFSM5FD4WIXA> . Triage notifications on the go with GitHub Mobile for iOS <https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675> or Android <https://play.google.com/store/apps/details?id=com.github.android&referrer=utm_campaign%3Dnotification-email%26utm_medium%3Demail%26utm_source%3Dgithub>.

-- Daniel Wheeler

[pavaninguva]

Hi Daniel, thanks for the quick reply.

It is also possible to include a diffusion term with those models, hence I wasnt too focused on the fact that many of these models are violently hyperbolic. How would you suggest I go about implementing those integral terms? Would the scipy route be a good first guess?

Best
Pavan

[guyer]

I can’t see the article for some reason, so I don’t know if there’s anything complicated with your integral, but I would start with `var.cellVolumeAverage * mesh.cellVolumes.sum()`. On Oct 1, 2021, at 3:30 PM, Pavan Inguva ***@***.******@***.***>> wrote: Hi Daniel, thanks for the quick reply. It is also possible to include a diffusion term with those models, hence I wasnt too focused on the fact that many of these models are violently hyperbolic. How would you suggest I go about implementing those integral terms? Would the scipy route be a good first guess? Best Pavan — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub<#824 (comment)>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/AAN66ROS4AG4GQDS2ML2SL3UEYD5XANCNFSM5FD4WIXA>. Triage notifications on the go with GitHub Mobile for iOS<https://gcc02.safelinks.protection.outlook.com/?url=https%3A%2F%2Fapps.apple.com%2Fapp%2Fapple-store%2Fid1477376905%3Fct%3Dnotification-email%26mt%3D8%26pt%3D524675&data=04%7C01%7Cjonathan.guyer%40nist.gov%7Cb78b1a23333443d694b808d98511f337%7C2ab5d82fd8fa4797a93e054655c61dec%7C1%7C0%7C637687134429405039%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=R2zmoJX4e5cUi4yJI4GLntn3RvgO8MfgBACFtc0NVEc%3D&reserved=0> or Android<https://gcc02.safelinks.protection.outlook.com/?url=https%3A%2F%2Fplay.google.com%2Fstore%2Fapps%2Fdetails%3Fid%3Dcom.github.android%26referrer%3Dutm_campaign%253Dnotification-email%2526utm_medium%253Demail%2526utm_source%253Dgithub&data=04%7C01%7Cjonathan.guyer%40nist.gov%7Cb78b1a23333443d694b808d98511f337%7C2ab5d82fd8fa4797a93e054655c61dec%7C1%7C0%7C637687134429405039%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=ktWC3B%2BQ%2FuMP1hJU%2Bv2JHg6WSEWp9%2FzHkWmv1VM0c84%3D&reserved=0>.

[pavaninguva]

Hi! Would like to ask a follow-up question.

How would I go about implementing the Mckendrick-von Foerster equation which has a funky bc

df/dt + df/da = -k(a) f, f(t,0) = \int_{0}^{\infty} b(a) f(t,a) da,

where b(a) is some sort of analytical function with respect to a.

I guess one strategy could be to include a explicit source term at the first node of the domain and compute the integral and pass it to the source? But that seems like quite an unelegant implementation. I am aware of the hyperbolic nature of this PDE, but the Van-Leer scheme seems to work quite well with this, so I would think FiPy should be able to handle it.

Thanks for the help!

[guyer]

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