The evolution seems to be of good quality, transitorious and those kind of impurities seem to be minimized and looks like this combination works fine.
Finally we wrote an experimental subroutine for the Tadmore approximation o the flux, which gave good results, but we did not went deep about it. Looks like a good approximation, but for short terms, the longer it evolves the worse it becomes. We need more experimentation to really have a fair opinion on this approximation, but we are learning....
The web site shows our evolutions.