Numerical investigations of the compressible Navier-Stokes system Bilal Al-Taki, Kevin Atsou, Jean-Jéróme Casanova, Thierry Goudon, Pauline Lafitte, Frédéric Lagoutière and Sebastian Minjeaud ESAIM: ProcS, 70 (2021) 1-13 Published online: 01 June 2021 DOI: 10.1051/proc/202107001