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Mathematics of Computation

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

 

 

Stable approximations for hyperbolic systems with moving internal boundary conditions


Authors: M. Goldberg and S. Abarbanel
Journal: Math. Comp. 28 (1974), 413-447
MSC: Primary 65N10
DOI: https://doi.org/10.1090/S0025-5718-1974-0381343-X
Corrigendum: Math. Comp. 29 (1975), 1167.
MathSciNet review: 0381343
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Abstract: The work of Kreiss on the stability theory of difference schemes for the mixed initial boundary value problem for linear hyperbolic systems is extended to deal with the case of the pure initial value problem with an internal boundary. The case of an internal boundary $ {X_B}$ that moves with constant speed c is treated, i.e., $ {X_B} = {X_0} + ct$. In particular, the stability of "hybrid" schemes is studied by using the Lax-Wendroff scheme at points that are not on the internal boundary, while using a first order accurate scheme at the internal boundary points. Numerical evidence is given that the results of the linear stability analysis describes the qualitative behavior of such schemes for nonlinear cases, when the internal boundary is a shock.


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DOI: https://doi.org/10.1090/S0025-5718-1974-0381343-X
Article copyright: © Copyright 1974 American Mathematical Society