Numerical stability for some equations of gas dynamics

Author:
A. Y. le Roux

Journal:
Math. Comp. **37** (1981), 307-320

MSC:
Primary 76N15; Secondary 65M10, 76A60

DOI:
https://doi.org/10.1090/S0025-5718-1981-0628697-8

MathSciNet review:
628697

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Abstract: The isentropic gas dynamics equations in Eulerian coordinates are expressed by means of the density $\rho$ and the momentum $q = \rho u$, instead of the velocity *u*, 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 ${L^\infty }$-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.

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Article copyright:
© Copyright 1981
American Mathematical Society