Stability of difference schemes in terms of Riemann invariants for a polytropic gas

The monotonicity and stability of a finite difference scheme with respect to initial data in the supremum norm are analyzed as applied to the polytropic gas equations written in terms of Riemann invariants for subsonic flows with $1<\gamma<3$. Conditions on the initial and boundary data are obtained under which subsonic flows with no shock waves develop in the medium. The theoretical conclusions are supported by numerical results.