Numerical stability for some equations of gas dynamics
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- by A. Y. le Roux PDF
- Math. Comp. 37 (1981), 307-320 Request permission
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.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- 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