Euler compare suggestions

[maojrs]

@ketch I took a look at Euler compare suggestions. I think the plots look really nice, and they show what we want to show. However, I think it would benefit from a bit more text and explanations.

• In the intro we should maybe add a brief intro to the shocktube problem and the blastwave problem since these are the examples we will use to compare the solutions.
• I am not really sure what you mean by fine solution in the plots. Is that the exact solution from the solver, or is it the solution computed with clawpack but with a very fine grid?
• Do we want to show all the code, or should we wrap it, so the user can only change the parameters that are relevant to them? Is the idea is that they go pyclaw all the way in this NB?
• An additional cool figure could be an interact that shows the analytic solution of one of the problems at a fixed time, along with the HLL and ROE approximation solutions, where the slider modifies the number of grid points.
• Maybe explain briefly what are high-order weno or at least add some references. We could also add the blastwave with Weno high-order?

I could help with some of this if you want.

[ketch]

Thanks! I opened a new PR with these changes.

In the intro we should maybe add a brief intro to the shocktube problem and the blastwave problem since these are the examples we will use to compare the solutions.

Done.

I am not really sure what you mean by fine solution in the plots. Is that the exact solution from the solver, or is it the solution computed with clawpack but with a very fine grid?

It's the latter; I added an explanation.

Do we want to show all the code, or should we wrap it, so the user can only change the parameters that are relevant to them? Is the idea is that they go pyclaw all the way in this NB?

Since this chapter is very different from all the rest, I've opted to show all the code. I added some text about this. I'm open to other suggestions.

An additional cool figure could be an interact that shows the analytic solution of one of the problems at a fixed time, along with the HLL and ROE approximation solutions, where the slider modifies the number of grid points.

I think this is a good idea but haven't done it yet. If you want to take a stab at it that would be great, or I may get to it in the next few days.

Maybe explain briefly what are high-order weno or at least add some references. We could also add the blastwave with Weno high-order?

I added a link to the most recent Clawpack paper, which has references to lots of other helpful material. I don't want to try to turn this chapter into an explanation of all the stuff we've left out of this book, so I stopped there.

Unfortunately, the blast wave problem with WENO5 leads to negative pressures unless you add a stronger limiter to enforce positivity.