@Article{CiCP-29-649,
author = {Spilimbergo , AlessandraF. Toro , Eleuterio and O. Müller , Lucas},
title = {One-Dimensional Blood Flow with Discontinuous Properties and Transport: Mathematical Analysis and Numerical Schemes},
journal = {Communications in Computational Physics},
year = {2021},
volume = {29},
number = {3},
pages = {649--697},
abstract = {<p style="text-align: justify;">In this paper we consider the one-dimensional blood flow model with discontinuous mechanical and geometrical properties, as well as passive scalar transport,
proposed in [E.F. Toro and A. Siviglia. Flow in collapsible tubes with discontinuous
mechanical properties: mathematical model and exact solutions. Communications in
Computational Physics. 13(2), 361-385, 2013], completing the mathematical analysis by
providing new propositions and new proofs of relations valid across different waves.
Next we consider a first order DOT Riemann solver, proposing an integration path that
incorporates the passive scalar and proving the well-balanced properties of the resulting numerical scheme for stationary solutions. Finally we describe a novel and simple
well-balanced, second order, non-linear numerical scheme to solve the equations under study; by using suitable test problems for which exact solutions are available, we
assess the well-balanced properties of the scheme, its capacity to provide accurate solutions in challenging flow conditions and its accuracy.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2020-0132},
url = {http://global-sci.org/intro/article_detail/cicp/18562.html}
}