Running the PPMP-Roe integration scheme with a lower cfl number (0.25) does alleviate the cross-patterns in the 2D sphere-wind test. (Also see the KH tests at the bottom of this post.
With the cfl number set to 0.4:
With the cfl number set to 0.25:
However, the implosion test at late times doesn’t look great with this integration scheme:
The unsplit methods do much better with this test, but the predictor-corrector scheme (VL) still doesn’t preserve symmetry. (This is an old problem, and as far as I could tell was not due to a bug, just something strange happening on the GPU).
That said, I was able to run a 2D cloud-wind test with the VL integrator (with dual energy and the H correction), and the result looks far more symmetric than the PPM-only integration.