Analysis of ray tube area in geometrical shock dynamics

We provide a rigorous analysis of structure of a ray tube in geometrical shock dynamics. Our aim is to shed more lights on the cross-sectional area function of a ray tube. We have shown that for a given ray tube and a given initial value of cross-sectional area, then its cross-sectional area can be...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 217; no. 2; pp. 830 - 836
Main Author: Zakeri, Gholam-Ali
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 15.09.2010
Elsevier
Subjects:
Cross sections
Cross-sectional area function
Dynamic structural analysis
Dynamic tests
Dynamics
Exact sciences and technology
Geometrical shock dynamics
Lie derivative
Mathematical analysis
Mathematical models
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
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Ray tube
Sciences and techniques of general use
Tubes
Wavefront
Lie derivative
Geometrical shock dynamics
Ray tube
Cross-sectional area function
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Wavefront
Numerical analysis
Boundary value problem
Applied mathematics
Initial value problem
Partial differential equation
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:We provide a rigorous analysis of structure of a ray tube in geometrical shock dynamics. Our aim is to shed more lights on the cross-sectional area function of a ray tube. We have shown that for a given ray tube and a given initial value of cross-sectional area, then its cross-sectional area can be determined uniquely everywhere. We give a definition of cross-sectional area of a ray tube in precise mathematical terms and from that we derive a set of relations, each describing the cross-sectional area for an arbitrary ray tube in geometrical shock dynamics. We have shown that from our results one can deduce Whitham’s area function relation as a partial differential equation from our general formulations. Some applications are discussed.
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2010.06.024