Testing plots and new collision operator in documentation

[joglekara]

See openjournals/joss-reviews#2182.

@TomGoffrey, @StanczakDominik , this is ready for review.

There are now 4 more plots in the manuscript as well as documentation. The need for illustrative tests resulted in the implementation of a new collision operator too, so a nice bonus!

[StanczakDominik]

Nice! I'll take a closer look later today :)

[TomGoffrey]

These look great.

Is the lack of momentum conservation with the Lenard-Bernstein operator for a drifting Maxwellian well known?

[joglekara]

Thanks @StanczakDominik :)

Great question @TomGoffrey . I think it is somewhat well known but I am happy to hear your thoughts too.

The reason I say it is somewhat well known is because the LB operator is constructed to have a solution of f(v) = exp(-v^2/2*v0^2) so it naturally relaxes to a driftless Maxwellian. I think the DG operator was conceived to address this directly, because it is a simple shift in the PDE that permits f(v) = exp(-(v-v_d)^2/v0^2) as a solution.

To add one more piece, the fully non-linear operator also relaxes to a driftless Maxwellian, but at a rate slower than given by the LB operator. So the answer, as always, is somewhere in the middle...