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Solutions of a nonhyperbolic pair of balance laws

Published online by Cambridge University Press:  15 March 2005

Michael Sever
Michael Sever*
Affiliation:
Department of Mathematics, The Hebrew University, Jerusalem, Israel. server@math.huji.ac.il
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Abstract

We describe a constructive algorithm for obtaining smooth solutions of a nonlinear, nonhyperbolic pair of balance laws modeling incompressible two-phase flow in one space dimension and time. Solutions are found as stationary solutions of a related hyperbolic system, based on the introduction of an artificial time variable. As may be expected for such nonhyperbolic systems, in general the solutions obtained do not satisfy both components of the given initial data. This deficiency may be overcome, however, by introducing an alternative “solution" satisfying both components of the initial data and an approximate form of a corresponding linearized system.

Keywords

Nonhyperbolic balance lawsincompressible two-fluid flow.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 1 , January 2005 , pp. 37 - 58
Copyright
© EDP Sciences, SMAI, 2005

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