Help modeling advection-diffusion equation with ModelingToolkit.jl

[ChrisRackauckas]

@juliohm

Can you share some recommendation on a good solver for this family of equations?

ROCK2 is a good one. Though I’m just going to fix the algorithm defaulter so that solve(prob) works here. That’s the best case scenario.

[ChrisRackauckas]

@juliohm

I think some of them are documented here along the corresponding MWE.

@xtalax can you highlight what areas this is hitting? I can help with the error hinting.

@juliohm

You mean that using t \in (0, 1) is unsupported? The code worked fine for me without the Interval constructor. It is a nice feature for those interested in “rectangular” domains made of Cartesian products of intervals.

It’s supposed to be . I mean it’s kind of okay for the interval case, but it breaks the uniformity.

[ChrisRackauckas]

@juliohm

Did you consider writing an intro book on the diffeq ecosystem to non-diffeq people?

Too much to do. I won’t have time for writing a book. There’s enough tutorials and documentation that it’s a book to write every week .

@juliohm

Which parts of the software already converged in terms of design?

The solvers. And well most of ModelingToolkit has converged, but as you can see from many other posts, it’s still in its last year of having major updates. MethodOfLines.jl in particular is the PDE feature of MTK, and it’s on the far edge of SciML right now. It’s exciting and it works, and from the Discourse we can see it’s had a lot of adoption even in its early stages, but it’s not robust yet. It’ll probably take another year for the PDE tools to really be complete. They are complete enough that it seems everyone can see the utility, but still incomplete enough that they aren’t “fully automated” with all of the nice error handling that we have everywhere else.

[juliohm]

@ChrisRackauckas

It’s supposed to be . I mean it’s kind of okay for the interval case, but it breaks the uniformity.

Makes sense. I think exporting Interval by default should make it more uniform and consistent.

@ChrisRackauckas

Too much to do. I won’t have time for writing a book. There’s enough tutorials and documentation that it’s a book to write every week .

In our case, we are pointing new GeoStats.jl’s users to the textbook. There they can learn the “correct” usage of the framework with more elaborated explanations, and have a glimpse of the bigger picture. It is a huge effort indeed, but after it is done, it can save the maintainers a lot of time. We are converting all the doc pages of our modules to simple lists of docstrings with minimum additional information.

Basically,

• Book => Explains “correct” usage and how things are connected conceptually
• Docs => Additional options for advanced users, a lookup table of docstrings

@ChrisRackauckas

It’ll probably take another year for the PDE tools to really be complete.

Fair enough. Looking forward to trying it more in this current project. Will share any issues we encounter along the way.

[ChrisRackauckas]

@juliohm

In our case, we are pointing new GeoStats.jl’s users to the textbook. There they can learn the “correct” usage of the framework with more elaborated explanations, and have a glimpse of the bigger picture. It is a huge effort indeed, but after it is done, it can save the maintainers a lot of time. We are converting all the doc pages of our modules to simple lists of docstrings with minimum additional information.

Basically,

• Book => Explains “correct” usage and how things are connected conceptually
• Docs => Additional options for advanced users, a lookup table of docstrings

I don’t disagree, I’ve just got a few jobs already , and more docs never hurts. But it’s an open market, good books are needed.

@juliohm

Makes sense. I think exporting Interval by default should make it more uniform and consistent.

We need to redo the domains stuff in general. It’s hitting some constraints as we’re generalizing.

[xtalax]

I think the MWE is failing due to lack of bcs, @juliohm did you see the solution interface page showing how to manipulate the solution? I agree that the docs could be improved.

[juliohm]

I have a working example now. The problem with the docs remains.

[ChrisRackauckas]

The docs were completely revamped with the upgrade to ModelingToolkit v9. This should be good now.