implement xsPPM7 reconstruction
This method is described in: Rider, Greenough, and Kamm (JCP, Vol. 225, 2, p. 1827-1848): https://ui.adsabs.harvard.edu/abs/2007JCoPh.225.1827R/abstract.
I tested this method in conjunction with RK2, but it requires a very low CFL number to be stable. It may work better with RK3.
The numerical dissipation is extremely low, so physical dissipation may be required for practical use. For instance, you cannot simulate a Sedov point explosion without extra dissipation.
Note: It requires the same number of ghost zones as PPM+flattening (4).
Edited by Ben Wibking