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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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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


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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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Math. Comp. 37 (1981), 307-320
  • MSC: Primary 76N15; Secondary 65M10, 76A60
  • DOI:
  • MathSciNet review: 628697