Numerical stability for some equations of gas dynamics

The isentropic gas dynamics equations in Eulerian coordinates are expressed by means of the density rho and the momentum q, instead of the velocity, in order to get domains bounded and invariant in the (rho, q)-plane for a wide class of pressure laws p(rho) and in the monodimensional case. A numerical scheme of the transport-projection type is proposed, which builds an approximate solution valued in such a domain. Since the characteristic speeds are bounded in this set, the stability condition is easily fulfilled and then estimates in the L-infinity-norm are derived at any time step. Similar results are extended to the model involving friction and topographical terms, and for a simplified model of supersonic flows. The nonapplication of this study to the gas dynamics in Lagrangian coordinates is shown.