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Flow in Collapsible Tubes with Discontinuous Mechanical Properties: Mathematical Model and Exact Solutions

Flow in Collapsible Tubes with Discontinuous Mechanical Properties: Mathematical Model and Exact Solutions
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Year:    2013

Communications in Computational Physics, Vol. 13 (2013), Iss. 2 : pp. 361–385

Abstract

We formulate a one-dimensional time-dependent non-linear mathematical model for some types of physiological fluid flow in collapsible tubes with discontinuous material properties. The resulting 6×6 hyperbolic system is analysed and the associated Riemann problem is solved exactly. Although the solution algorithm deals with idealised cases, it is nonetheless uniquely well-suited for assessing the performance of numerical methods intended for simulating more general situations. Moreover, our model may be a useful starting point for numerical calculations of realistic flows involving rapid and discontinuous material property variations. One important example in mind is the simulation of blood flow in medium-to-large veins in humans. Finally, we also discuss some peculiarities of the model regarding the loss of strict hyperbolicity and uniqueness. In particular we show an example in which the solution of the Riemann problem is non unique. 

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.210611.240212a

Communications in Computational Physics, Vol. 13 (2013), Iss. 2 : pp. 361–385

Published online:    2013-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:   

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