Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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
MathSciNet review: 628697
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 76N15, 65M10, 76A60

Retrieve articles in all journals with MSC: 76N15, 65M10, 76A60

Additional Information

Article copyright: © Copyright 1981 American Mathematical Society