TY - JOUR
T1 - One-Dimensional Blood Flow with Discontinuous Properties and Transport: Mathematical Analysis and Numerical Schemes
AU - Spilimbergo , Alessandra
AU - F. Toro , Eleuterio
AU - O. Müller , Lucas
JO - Communications in Computational Physics
VL - 3
SP - 649
EP - 697
PY - 2021
DA - 2021/01
SN - 29
DO - http://doi.org/10.4208/cicp.OA-2020-0132
UR - https://global-sci.org/intro/article_detail/cicp/18562.html
KW - Blood flows, Riemann problem, wave relations, finite volume method, well-balancing.
AB - <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>