Errors of linear Alfven wave for RK3+PPM (xorder=3) are much smaller than those in Athena++ paper

[takasao]

When I performed the convergence test of MHD linear waves, I noticed that my errors of Alfven waves for RK3+PPM (xorder=3) are much smaller than those in Athena++ paper (Stone+20). I’m curious about the reason. Do you have any ideas?

Below is Figure 11 of Stone+20. The error of Alfven wave is O(1e-7) when Nx=16 and RK3+PPM:

Below is my results. Please compare data for RK3+PPM (xorder=3, orange squares) in the upper right panel with those in the previous figure. The error is O(1e-9) when Nx=16.

I haven't checked old versions of the code to find the reason.

The unexpected behavior for RK3+PPM (xorder=4, 4c) is related to #535.