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Boundary Conditions for Suppressing Rapidly Moving Components in Hyperbolic Systems

Robert L. Higdon
SIAM Journal on Numerical Analysis
Vol. 21, No. 3 (Jun., 1984), pp. 413-432
Stable URL: http://www.jstor.org/stable/2157060
Page Count: 20
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Boundary Conditions for Suppressing Rapidly Moving Components in Hyperbolic Systems
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Abstract

This work is concerned with hyperbolic systems of partial differential equations for which certain of the associated propagation speeds are a great deal larger than the other propagation speeds. Our goal is to find boundary conditions which prevent rapidly moving waves from entering the given spatial domain. Conditions of this type are desirable in certain numerical computations arising in meteorology. In order to find these conditions, we first transform the given system to an approximate diagonal form in such a way that each of the new dependent variables can be identified as a slow, incoming fast, or outgoing fast component of the solution. We then find local boundary conditions which suppress the incoming fast part. We consider only linear systems. These methods are applied in detail to the linearized shallow water equations. The results of numerical tests of various boundary conditions are included.

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