Numerical stability for some equations of gas dynamics
Abstract
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 transportprojection 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 Linfinitynorm 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.
 Publication:

Mathematics of Computation
 Pub Date:
 October 1981
 Bibcode:
 1981MaCom..37..307L
 Keywords:

 Computational Fluid Dynamics;
 Flow Equations;
 Gas Dynamics;
 Isentropic Processes;
 Numerical Stability;
 Supersonic Flow;
 Cauchy Problem;
 Euler Equations Of Motion;
 Hyperbolic Differential Equations;
 Lagrange Coordinates;
 Mathematical Models;
 Parabolic Differential Equations;
 Fluid Mechanics and Heat Transfer