Are there any accessible (both physically and intellectually) examples of modelling a recognisibly real world problem*?

Any type would be good, but specifically a magneto-dynamic would be most useful.

*By which I mean, an example that starts with a description – with maybe some pictures – of a real world problem to solve, before diving into a mathematical representation of that, that may be of interest to those writing FreeFEM, but is of little interest to those trying to /use/ it.

A real world description: Find the minimum sized toroidal core running as a 1:17 transformer (7.4V to 125V/0.5A @145kHz) to avoid overheating (say: < 40°C rise).

You problem is not a simulation problem due to the material propriety at level of thermic, conductivity, …
You have to say we use : copper, iron, ??? all material , and after we can try to solve the problem if you are able to give a mathematical modelization.

First, thanks for the reply. I’d given up on getting one.

The problem as defined, is a real description of an actual problem; in the terms that I as an engineer understand it.

The coils are obviously copper; the core can be any of a range of materials from a vast range of ferrites, sintered metal powders(eg.Molypermalloy(Fe-Ni-Mo), High Flux:(Fe-Ni),KoolMu(Fe-Al-Si), XFlux(Fe-Si), KoolMuMax(Fe-Si-Al), Wound amourphuos iron ribbon(Metallic Glass) etc.) and I know I will have to obtain the material specs.-- BH curve, inital permability, los angle etc.) for each core type I wish to try. As I have do for FEMM.

It can be simulated. This is a 2D simulation done using FEMM, and what it looks like physically:

The problem is that a 2D simulation does not allow correct assessment of both loss (hysteresis, skin & proximity effects, core) and saturation levels when working with toroids with near square areal cross section; because there is only a single value for the depth of the simulation, and one number cannot account for both the actual cross section and the true turn length simultaneously.

I’m not asking anyone to solve my particular problem!

What I’m looking for is a fully worked example that starts with a physical description and shows me step by step how to construct or import the geometry & mesh it; setup the material specifications; select the appropriate solver/formulae; run the simulation; export the results and view them.

My impression having looked at the available examples is that it may be that freeFEM is not intended for use outside of acadamia. If that is the case, then I best look elsewhere.

As an engineer (not a mathematician) I look to software like FreeFem to perform the calculations that are beyond my knowledge and remit. If I have to become a mathematician in order to couch by problem definition as a mathematical modelization, I probably wouldn’t need to use FreeFem to perform the calculations!

Is FreeFem not capable of dealing with real world problems?

I can generate a mesh for my model; though I’d need guidance about what type of mesh and how fine FreeFem requires.

And I don’t mind ‘computationally expensive’. I can run it for as long as it takes, provided I have a reasonable expectation of it producing the results I need.

A worked example or two would go a long way to giving some confidence that I can start with a problem in terms I understand, and end up with a solution that is recognisible as such.

The bit that troubles me is “After you have the formulation to solve the problem”. The documentation, and your replies all lead me to believe that I would need to provide the math required to perform the simulation.