Volume 29, Issue 3
One-Dimensional Blood Flow with Discontinuous Properties and Transport: Mathematical Analysis and Numerical Schemes

Alessandra Spilimbergo, Eleuterio F. Toro & Lucas O. Müller

Commun. Comput. Phys., 29 (2021), pp. 649-697.

Published online: 2021-01

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  • Abstract

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.

  • Keywords

Blood flows, Riemann problem, wave relations, finite volume method, well-balancing.

  • AMS Subject Headings

76Z05, 35L02, 65M08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-29-649, author = {Spilimbergo , Alessandra and F. 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 = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0132}, url = {http://global-sci.org/intro/article_detail/cicp/18562.html} }
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 -

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.

Alessandra Spilimbergo, Eleuterio F. Toro & Lucas O. Müller. (2021). One-Dimensional Blood Flow with Discontinuous Properties and Transport: Mathematical Analysis and Numerical Schemes. Communications in Computational Physics. 29 (3). 649-697. doi:10.4208/cicp.OA-2020-0132
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