Numerical Stability for Some Equations
نویسنده
چکیده
The isentropic gas dynamics equations in Eulerian coordinates are expressed by means of the density p and the momentum q = pu, instead of the velocity u, in order to get domains bounded and invariant in the (p. <?)-plane, for a wide class of pressure laws p(p) 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°°-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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