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I am looking for a method to automatically solve custom PDEs on a custom control volume. Specifically I would like to solve equations similar (but not exactly alike) to:

$$\frac{\partial y}{\partial t} = \frac{\partial^2}{\partial x} y^n + A \frac{\partial y}{\partial x}.$$

According to what I read this is what OpenFOAM is for. The problem is that I cannot find a comprehensive guide on how to program things like this is OpenFOAM.

According to the only answer for this question there wasn't, indeed, such a guide by the time that answer was posted. (apart from a small review that doesn't aim to teach)

Now, however, it is three years later and I'm thinking there might be more documentation about it.

So my question is: is OpenFOAM really the best approach for what I want or are there better ways of doing this? If it is the best approach, is a there now a guide on how to do this?

Thank you.

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I think OpenFOAM is pretty well suited for these problems; however, the best place to send your questions are to the CFD forum where much of the OPF community resides.

You might also find some more guidance here.

I recommend starting with something simple, like this example, to learn how to program your PDE.

Lastly, I would comment that there is no, strictly speaking, best approach to this kind of problem. OpenFOAM has a number of numerical techniques available to you as problems become stiffer and more difficult. In addition, you have a number of pre-processing tools at your disposal. The disadvantage is that it has a modest learning curve and it is developed by the CFD community, which has different needs. On this note, you might consider a tools such as futureye or MOOSE. For your application, MOOSE would be my recommended choice.

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