ITLApplied  Computational Mathematics Division
ACMD Seminar Series
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Singular Shocks in a Two-Fluid Model for Bubbly Flows

Barbara Keyfitz
Department of Mathematics, University of Houston

Monday, April 29, 2002 15:00-16:00,
Room 145, NIST North (820)
Monday, April 29, 2002 13:00-14:00,
Room 4550

Abstract: In a number of physical and engineering systems, the result of basic modeling is a system of equations of non-hyperbolic type: these are equations whose linearizations are, in effect, meaningless vis a vis the character of the physical problem at hand. The user community has been uncertain about how to treat these models but there is a simple mathematical explanation: the models may be an incomplete (rather than incorrect) description of the physical phenomenon. In this talk I will outline some models which arise in two-phase flow, and show how an analysis of the nonlinear nonhyperbolic operator can be undertaken using conservation law theory. A novel kind of weak solution -- a so-called singular shock -- appears in solving Riemann problems for this operator. Recent work of Michael Sever, which I will describe, sheds light on the nature of these singular shocks. Using these solutions, one can say that the models predict phenomena which are consistent with the physical considerations that went into their derivation.
Contact: A. J. Kearsley

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