Close Search Advanced
Journals
Resources
About Us
Open Access

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
Preview
Add to basket

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. 

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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:   

  1. Low-Shapiro hydrostatic reconstruction technique for blood flow simulation in large arteries with varying geometrical and mechanical properties

    Ghigo, A.R. | Delestre, O. | Fullana, J.-M. | Lagrée, P.-Y.

    Journal of Computational Physics, Vol. 331 (2017), Iss. P.108

    https://doi.org/10.1016/j.jcp.2016.11.032 [Citations: 16]

  2. Numerical coupling of 0D and 1D models in networks of vessels including transonic flow conditions. Application to short‐term transient and stationary hemodynamic simulation of postural changes

    Murillo, Javier | García‐Navarro, Pilar

    International Journal for Numerical Methods in Biomedical Engineering, Vol. 39 (2023), Iss. 11

    https://doi.org/10.1002/cnm.3751 [Citations: 0]

  3. High-Order Fully Well-Balanced Numerical Methods for One-Dimensional Blood Flow with Discontinuous Properties

    Pimentel-García, Ernesto | Müller, Lucas O. | Toro, Eleuterio F. | Parés, Carlos

    SSRN Electronic Journal , Vol. (2022), Iss.

    https://doi.org/10.2139/ssrn.4147172 [Citations: 0]

  4. Comparison of inviscid and viscid one-dimensional models of blood flow in arteries

    Krivovichev, Gerasim V.

    Applied Mathematics and Computation, Vol. 418 (2022), Iss. P.126856

    https://doi.org/10.1016/j.amc.2021.126856 [Citations: 2]

  5. AENO: a Novel Reconstruction Method in Conjunction with ADER Schemes for Hyperbolic Equations

    Toro, Eleuterio F. | Santacá, Andrea | Montecinos, Gino I. | Celant, Morena | Müller, Lucas O.

    Communications on Applied Mathematics and Computation, Vol. 5 (2023), Iss. 2 P.776

    https://doi.org/10.1007/s42967-021-00147-0 [Citations: 7]

  6. On the Effects of Boundary Conditions in One-Dimensional Models of Hemodynamics

    Krivovichev, Gerasim V.

    Mathematics, Vol. 10 (2022), Iss. 21 P.4058

    https://doi.org/10.3390/math10214058 [Citations: 1]

  7. A high‐order local time stepping finite volume solver for one‐dimensional blood flow simulations: application to the ADAN model

    Müller, Lucas O. | Blanco, Pablo J. | Watanabe, Sansuke M. | Feijóo, Raúl A.

    International Journal for Numerical Methods in Biomedical Engineering, Vol. 32 (2016), Iss. 10

    https://doi.org/10.1002/cnm.2761 [Citations: 32]

  8. Well-balanced high-order numerical schemes for one-dimensional blood flow in vessels with varying mechanical properties

    Müller, Lucas O. | Parés, Carlos | Toro, Eleuterio F.

    Journal of Computational Physics, Vol. 242 (2013), Iss. P.53

    https://doi.org/10.1016/j.jcp.2013.01.050 [Citations: 91]

  9. High-order fully well-balanced numerical methods for one-dimensional blood flow with discontinuous properties

    Pimentel-García, Ernesto | Müller, Lucas O. | Toro, Eleuterio F. | Parés, Carlos

    Journal of Computational Physics, Vol. 475 (2023), Iss. P.111869

    https://doi.org/10.1016/j.jcp.2022.111869 [Citations: 8]

  10. Letter Re: Internal jugular and vertebral vein volume flow in patients with clinically isolated syndrome or mild multiple sclerosis and healthy controls: results from a prospective sonographer-blinded study

    Sisini, Francesco | Taibi, Angelo | Gambaccini, Mauro | Zamboni, Paolo

    Phlebology: The Journal of Venous Disease, Vol. 29 (2014), Iss. 8 P.536

    https://doi.org/10.1177/0268355513518912 [Citations: 1]

  11. Uncertainty quantification methodology for hyperbolic systems with application to blood flow in arteries

    Petrella, M. | Tokareva, S. | Toro, E.F.

    Journal of Computational Physics, Vol. 386 (2019), Iss. P.405

    https://doi.org/10.1016/j.jcp.2019.02.013 [Citations: 7]

  12. A Solution of the Junction Riemann Problem for 1D Hyperbolic Balance Laws in Networks including Supersonic Flow Conditions on Elastic Collapsible Tubes

    Murillo, Javier | García-Navarro, Pilar

    Symmetry, Vol. 13 (2021), Iss. 9 P.1658

    https://doi.org/10.3390/sym13091658 [Citations: 5]

  13. A Direct Eulerian GRP Scheme for a Blood Flow Model in Arteries

    Sheng, Wancheng | Zhang, Qinglong | Zheng, Yuxi

    SIAM Journal on Scientific Computing, Vol. 43 (2021), Iss. 3 P.A1975

    https://doi.org/10.1137/19M1284476 [Citations: 6]

  14. Formulation of exactly balanced solvers for blood flow in elastic vessels and their application to collapsed states

    Murillo, J. | Navas-Montilla, A. | García-Navarro, P.

    Computers & Fluids, Vol. 186 (2019), Iss. P.74

    https://doi.org/10.1016/j.compfluid.2019.04.008 [Citations: 13]

  15. Geometric multiscale modeling of the cardiovascular system, between theory and practice

    Quarteroni, A. | Veneziani, A. | Vergara, C.

    Computer Methods in Applied Mechanics and Engineering, Vol. 302 (2016), Iss. P.193

    https://doi.org/10.1016/j.cma.2016.01.007 [Citations: 146]

  16. Bounds for Wave Speeds in the Riemann Problem: Direct Theoretical Estimates

    Toro, E.F. | Müller, L.O. | Siviglia, A.

    Computers & Fluids, Vol. 209 (2020), Iss. P.104640

    https://doi.org/10.1016/j.compfluid.2020.104640 [Citations: 26]

  17. TV-HLL Solver for One-Dimensional Fluid Flow Inside Elastic Vessels

    Kapen, Pascalin Tiam | Tchuen, Ghislain

    International Journal of Applied and Computational Mathematics, Vol. 3 (2017), Iss. 2 P.905

    https://doi.org/10.1007/s40819-016-0187-2 [Citations: 1]

  18. Evaluation effect of magnetic field on nanofluid flow through a deformable bifurcated arterial network

    Chapal Hossain, S.M. | Zhang, Xin | Liu, Zhifeng | Haider, Zeeshan | Memon, Kashan | Panhwar, Fazil | Mbogba, Momoh karmah | Hu, Peng | Zhao, Gang

    International Communications in Heat and Mass Transfer, Vol. 98 (2018), Iss. P.239

    https://doi.org/10.1016/j.icheatmasstransfer.2018.09.004 [Citations: 13]

  19. On the exact solution of the Riemann problem for blood flow in human veins, including collapse

    Spiller, C. | Toro, E.F. | Vázquez-Cendón, M.E. | Contarino, C.

    Applied Mathematics and Computation, Vol. 303 (2017), Iss. P.178

    https://doi.org/10.1016/j.amc.2017.01.024 [Citations: 7]

  20. Analytical solutions of the problems for equations of one-dimensional hemodynamics

    Tkachenko, P S | Krivovichev, G V

    Journal of Physics: Conference Series, Vol. 1400 (2019), Iss. 4 P.044031

    https://doi.org/10.1088/1742-6596/1400/4/044031 [Citations: 1]

  21. Numerical investigation of three-dimensional incompressible fluid flow in curved elastic tube

    Ni, Peng | Fang, Dehong | Ai, Li

    Journal of Intelligent Construction, Vol. 2 (2024), Iss. 3 P.9180023

    https://doi.org/10.26599/JIC.2024.9180023 [Citations: 1]

  22. A semi-implicit finite volume scheme for blood flow in elastic and viscoelastic vessels

    Lucca, A. | Busto, S. | Müller, L.O. | Toro, E.F. | Dumbser, M.

    Journal of Computational Physics, Vol. 495 (2023), Iss. P.112530

    https://doi.org/10.1016/j.jcp.2023.112530 [Citations: 2]

  23. Enhanced global mathematical model for studying cerebral venous blood flow

    Müller, Lucas O. | Toro, Eleuterio F.

    Journal of Biomechanics, Vol. 47 (2014), Iss. 13 P.3361

    https://doi.org/10.1016/j.jbiomech.2014.08.005 [Citations: 62]

  24. Computational haemodynamics in stenotic internal jugular veins

    Caiazzo, Alfonso | Montecinos, Gino | Müller, Lucas O. | Haacke, E. Mark | Toro, Eleuterio F.

    Journal of Mathematical Biology, Vol. 70 (2015), Iss. 4 P.745

    https://doi.org/10.1007/s00285-014-0778-7 [Citations: 14]

  25. Elastic jump propagation across a blood vessel junction

    Spelman, Tamsin A. | Onah, Ifeanyi S. | MacTaggart, David | Stewart, Peter S.

    Royal Society Open Science, Vol. 11 (2024), Iss. 7

    https://doi.org/10.1098/rsos.232000 [Citations: 0]

  26. Fluid mechanical modeling of the upper urinary tract

    Zheng, Shaokai | Carugo, Dario | Mosayyebi, Ali | Turney, Ben | Burkhard, Fiona | Lange, Dirk | Obrist, Dominik | Waters, Sarah | Clavica, Francesco

    WIREs Mechanisms of Disease, Vol. 13 (2021), Iss. 6

    https://doi.org/10.1002/wsbm.1523 [Citations: 21]

  27. The splitting-based semi-implicit finite-difference schemes for simulation of blood flow in arteries

    Krivovichev, Gerasim V.

    Computers & Fluids, Vol. 266 (2023), Iss. P.106049

    https://doi.org/10.1016/j.compfluid.2023.106049 [Citations: 0]

  28. A fast method for solving a linear model of one-dimensional blood flow in a viscoelastic arterial tree

    Korade, Ivan | Virag, Zdravko | Krizmanić, Severino

    Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, Vol. 231 (2017), Iss. 3 P.203

    https://doi.org/10.1177/0954411916688718 [Citations: 1]

  29. Computational analysis of one-dimensional models for simulation of blood flow in vascular networks

    Krivovichev, Gerasim V.

    Journal of Computational Science, Vol. 62 (2022), Iss. P.101705

    https://doi.org/10.1016/j.jocs.2022.101705 [Citations: 8]

  30. Computational hemodynamics in arteries with the one-dimensional augmented fluid-structure interaction system: viscoelastic parameters estimation and comparison with in-vivo data

    Bertaglia, Giulia | Navas-Montilla, Adrián | Valiani, Alessandro | Monge García, Manuel Ignacio | Murillo, Javier | Caleffi, Valerio

    Journal of Biomechanics, Vol. 100 (2020), Iss. P.109595

    https://doi.org/10.1016/j.jbiomech.2019.109595 [Citations: 19]

  31. Numerical Study of Fluid-Structure Interaction for Blood Flow in Human Viscoelastic Artery

    Mal, Tarak Nath | Soni, Bharat | Nayak, Ameeya Kumar

    Proceeding of Proceedings of the 27th National and 5th International ISHMT-ASTFE Heat and Mass Transfer Conference December 14-17, 2023, IIT Patna, Patna-801106, Bihar, India, (2024), P.167

    https://doi.org/10.1615/IHMTC-2023.280 [Citations: 0]
  32. Modeling of Mass Transport Processes in Biological Media

    Hybrid-dimensional models for blood flow and mass transport: Sequential and embedded 3D-1D models

    Formaggia, Luca | Zunino, Paolo

    2022

    https://doi.org/10.1016/B978-0-323-85740-6.00005-4 [Citations: 0]

  33. ENO-ET: a reconstruction scheme based on extended ENO stencil and truncated highest-order term

    Montecinos, Gino I. | Toro, Eleuterio F.

    Applied Mathematics and Computation, Vol. 442 (2023), Iss. P.127742

    https://doi.org/10.1016/j.amc.2022.127742 [Citations: 0]

  34. Brain venous haemodynamics, neurological diseases and mathematical modelling. A review

    Toro, Eleuterio F.

    Applied Mathematics and Computation, Vol. 272 (2016), Iss. P.542

    https://doi.org/10.1016/j.amc.2015.06.066 [Citations: 28]

  35. Construction of hybrid 1D‐0D networks for efficient and accurate blood flow simulations

    Ghitti, Beatrice | Blanco, Pablo J. | Toro, Eleuterio F. | Müller, Lucas O.

    International Journal for Numerical Methods in Fluids, Vol. 95 (2023), Iss. 2 P.262

    https://doi.org/10.1002/fld.5149 [Citations: 4]

  36. A fully well-balanced scheme for the 1D blood flow equations with friction source term

    Ghitti, Beatrice | Berthon, Christophe | Le, Minh Hoang | Toro, Eleuterio F.

    Journal of Computational Physics, Vol. 421 (2020), Iss. P.109750

    https://doi.org/10.1016/j.jcp.2020.109750 [Citations: 21]

  37. A Limiting Viscosity Approach to the Riemann Problem in Blood Flow Through Artery

    Mondal, Rakib |

    Bulletin of the Malaysian Mathematical Sciences Society, Vol. 46 (2023), Iss. 6

    https://doi.org/10.1007/s40840-023-01579-y [Citations: 1]

  38. A global multiscale mathematical model for the human circulation with emphasis on the venous system

    Müller, Lucas O. | Toro, Eleuterio F.

    International Journal for Numerical Methods in Biomedical Engineering, Vol. 30 (2014), Iss. 7 P.681

    https://doi.org/10.1002/cnm.2622 [Citations: 174]

  39. Interactions of stationary wave with rarefaction wave and shock wave for a blood flow model in arteries

    Sheng, Wancheng | Xu, Shufang

    Zeitschrift für angewandte Mathematik und Physik, Vol. 75 (2024), Iss. 4

    https://doi.org/10.1007/s00033-024-02295-8 [Citations: 0]

  40. A benchmark study of numerical schemes for one‐dimensional arterial blood flow modelling

    Boileau, Etienne | Nithiarasu, Perumal | Blanco, Pablo J. | Müller, Lucas O. | Fossan, Fredrik Eikeland | Hellevik, Leif Rune | Donders, Wouter P. | Huberts, Wouter | Willemet, Marie | Alastruey, Jordi

    International Journal for Numerical Methods in Biomedical Engineering, Vol. 31 (2015), Iss. 10

    https://doi.org/10.1002/cnm.2732 [Citations: 147]

  41. Well‐balanced high‐order solver for blood flow in networks of vessels with variable properties

    Müller, Lucas O. | Toro, Eleuterio F.

    International Journal for Numerical Methods in Biomedical Engineering, Vol. 29 (2013), Iss. 12 P.1388

    https://doi.org/10.1002/cnm.2580 [Citations: 88]

  42. Second-order well-balanced Lagrange-projection schemes for blood flow equations

    Del Grosso, A. | Chalons, C.

    Calcolo, Vol. 58 (2021), Iss. 4

    https://doi.org/10.1007/s10092-021-00434-5 [Citations: 4]

  43. A global mathematical model for the simulation of stenoses and bypass placement in the human arterial system

    Strocchi, M. | Contarino, C. | Zhang, Q. | Bonmassari, R. | Toro, E.F.

    Applied Mathematics and Computation, Vol. 300 (2017), Iss. P.21

    https://doi.org/10.1016/j.amc.2016.11.028 [Citations: 4]

  44. Modeling blood flow in viscoelastic vessels: the 1D augmented fluid–structure interaction system

    Bertaglia, Giulia | Caleffi, Valerio | Valiani, Alessandro

    Computer Methods in Applied Mechanics and Engineering, Vol. 360 (2020), Iss. P.112772

    https://doi.org/10.1016/j.cma.2019.112772 [Citations: 31]

  45. Flux vector splitting schemes applied to a conservative 1D blood flow model with transport for arteries and veins

    Spilimbergo, Alessandra | Toro, Eleuterio F. | Siviglia, Annunziato | Müller, Lucas O.

    Computers & Fluids, Vol. 271 (2024), Iss. P.106165

    https://doi.org/10.1016/j.compfluid.2023.106165 [Citations: 1]

  46. Multiscale Constitutive Framework of One-Dimensional Blood Flow Modeling: Asymptotic Limits and Numerical Methods

    Bertaglia, Giulia | Pareschi, Lorenzo

    Multiscale Modeling & Simulation, Vol. 21 (2023), Iss. 3 P.1237

    https://doi.org/10.1137/23M1554230 [Citations: 0]

  47. Hyperbolic reformulation of a 1D viscoelastic blood flow model and ADER finite volume schemes

    Montecinos, Gino I. | Müller, Lucas O. | Toro, Eleuterio F.

    Journal of Computational Physics, Vol. 266 (2014), Iss. P.101

    https://doi.org/10.1016/j.jcp.2014.02.013 [Citations: 55]

  48. Variable separated physics-informed neural networks based on adaptive weighted loss functions for blood flow model

    Liu, Youqiong | Cai, Li | Chen, Yaping | Ma, Pengfei | Zhong, Qian

    Computers & Mathematics with Applications, Vol. 153 (2024), Iss. P.108

    https://doi.org/10.1016/j.camwa.2023.11.018 [Citations: 3]

  49. High resolution methods for scalar transport problems in compliant systems of arteries

    Tavelli, M. | Dumbser, M. | Casulli, V.

    Applied Numerical Mathematics, Vol. 74 (2013), Iss. P.62

    https://doi.org/10.1016/j.apnum.2013.06.009 [Citations: 12]

  50. A one‐dimensional computational model for blood flow in an elastic blood vessel with a rigid catheter

    Pradhan, Aseem Milind | Mut, Fernando | Cebral, Juan Raul

    International Journal for Numerical Methods in Biomedical Engineering, Vol. 40 (2024), Iss. 7

    https://doi.org/10.1002/cnm.3834 [Citations: 1]

  51. Study of pulse wave phenomena associated with blood flow model in human viscoelastic artery

    Mal, Tarak Nath | Soni, Bharat | Nayak, Ameeya Kumar

    Physics of Fluids, Vol. 36 (2024), Iss. 4

    https://doi.org/10.1063/5.0189980 [Citations: 2]

  52. Total Effective Vascular Compliance of a Global Mathematical Model for the Cardiovascular System

    Celant, Morena | Toro, Eleuterio F. | Müller, Lucas O.

    Symmetry, Vol. 13 (2021), Iss. 10 P.1858

    https://doi.org/10.3390/sym13101858 [Citations: 4]

  53. Modeling essential hypertension with a closed‐loop mathematical model for the entire human circulation

    Celant, Morena | Toro, Eleuterio F. | Bertaglia, Giulia | Cozzio, Susanna | Caleffi, Valerio | Valiani, Alessandro | Blanco, Pablo J. | Müller, Lucas O.

    International Journal for Numerical Methods in Biomedical Engineering, Vol. 39 (2023), Iss. 11

    https://doi.org/10.1002/cnm.3748 [Citations: 2]

  54. The initial-boundary problem for the system of 1D equations of non-Newtonian hemodynamics

    Krivovichev, Gerasim V

    Journal of Physics: Conference Series, Vol. 1697 (2020), Iss. 1 P.012075

    https://doi.org/10.1088/1742-6596/1697/1/012075 [Citations: 0]

  55. Consistent treatment of viscoelastic effects at junctions in one-dimensional blood flow models

    Müller, Lucas O. | Leugering, Günter | Blanco, Pablo J.

    Journal of Computational Physics, Vol. 314 (2016), Iss. P.167

    https://doi.org/10.1016/j.jcp.2016.03.012 [Citations: 28]

  56. Simulation of one‐dimensional blood flow in networks of human vessels using a novel TVD scheme

    Huang, P. G. | Muller, L. O.

    International Journal for Numerical Methods in Biomedical Engineering, Vol. 31 (2015), Iss. 5

    https://doi.org/10.1002/cnm.2701 [Citations: 25]
  57. Handbook of Numerical Methods for Hyperbolic Problems - Basic and Fundamental Issues

    The Riemann Problem

    Toro, E.F.

    2016

    https://doi.org/10.1016/bs.hna.2016.09.015 [Citations: 6]

  58. Junction-Generalized Riemann Problem for stiff hyperbolic balance laws in networks: An implicit solver and ADER schemes

    Contarino, Christian | Toro, Eleuterio F. | Montecinos, Gino I. | Borsche, Raul | Kall, Jochen

    Journal of Computational Physics, Vol. 315 (2016), Iss. P.409

    https://doi.org/10.1016/j.jcp.2016.03.049 [Citations: 16]

  59. ADER scheme with a simplified solver for the generalized Riemann problem and an average ENO reconstruction procedure. Application to blood flow

    Montecinos, Gino I. | Santacá, Andrea | Celant, Morena | Müller, Lucas O. | Toro, Eleuterio F.

    Computers & Fluids, Vol. 248 (2022), Iss. P.105685

    https://doi.org/10.1016/j.compfluid.2022.105685 [Citations: 5]

  60. Seven Mathematical Models of Hemorrhagic Shock

    Curcio, Luciano | D'Orsi, Laura | De Gaetano, Andrea | Korobeinikov, Andrei

    Computational and Mathematical Methods in Medicine, Vol. 2021 (2021), Iss. P.1

    https://doi.org/10.1155/2021/6640638 [Citations: 3]

  61. A one-dimensional mathematical model of collecting lymphatics coupled with an electro-fluid-mechanical contraction model and valve dynamics

    Contarino, Christian | Toro, Eleuterio F.

    Biomechanics and Modeling in Mechanobiology, Vol. 17 (2018), Iss. 6 P.1687

    https://doi.org/10.1007/s10237-018-1050-7 [Citations: 17]

  62. Tube law parametrization using in vitro data for one‐dimensional blood flow in arteries and veins

    Colombo, Chiara | Siviglia, Annunziato | Toro, Eleuterio F. | Bia, Daniel | Zócalo, Yanina | Müller, Lucas O.

    International Journal for Numerical Methods in Biomedical Engineering, Vol. 40 (2024), Iss. 4

    https://doi.org/10.1002/cnm.3803 [Citations: 0]

  63. Multiple states for flow through a collapsible tube with discontinuities

    Siviglia, A. | Toffolon, M.

    Journal of Fluid Mechanics, Vol. 761 (2014), Iss. P.105

    https://doi.org/10.1017/jfm.2014.635 [Citations: 8]

  64. Steady analysis of transcritical flows in collapsible tubes with discontinuous mechanical properties: implications for arteries and veins

    Siviglia, A. | Toffolon, M.

    Journal of Fluid Mechanics, Vol. 736 (2013), Iss. P.195

    https://doi.org/10.1017/jfm.2013.542 [Citations: 15]

  65. A Roe type energy balanced solver for 1D arterial blood flow and transport

    Murillo, J. | García-Navarro, P.

    Computers & Fluids, Vol. 117 (2015), Iss. P.149

    https://doi.org/10.1016/j.compfluid.2015.05.003 [Citations: 18]

  66. Riemann problem and Godunov-type scheme for a two-layer blood flow model

    Zhang, Qinglong | Sheng, Wancheng | Xiao, Tao

    Applied Mathematics Letters, Vol. 135 (2023), Iss. P.108437

    https://doi.org/10.1016/j.aml.2022.108437 [Citations: 6]

  67. Modeling blood flow in networks of viscoelastic vessels with the 1-D augmented fluid–structure interaction system

    Piccioli, Francesco | Bertaglia, Giulia | Valiani, Alessandro | Caleffi, Valerio

    Journal of Computational Physics, Vol. 464 (2022), Iss. P.111364

    https://doi.org/10.1016/j.jcp.2022.111364 [Citations: 19]

  68. Uncertainty quantification of viscoelastic parameters in arterial hemodynamics with the a-FSI blood flow model

    Bertaglia, Giulia | Caleffi, Valerio | Pareschi, Lorenzo | Valiani, Alessandro

    Journal of Computational Physics, Vol. 430 (2021), Iss. P.110102

    https://doi.org/10.1016/j.jcp.2020.110102 [Citations: 14]

  69. Impact of CCSVI on cerebral haemodynamics: a mathematical study using MRI angiographic and flow data

    Müller, LO | Toro, EF | Haacke, EM | Utriainen, D

    Phlebology: The Journal of Venous Disease, Vol. 31 (2016), Iss. 5 P.305

    https://doi.org/10.1177/0268355515586526 [Citations: 15]

  70. Cerebrospinal fluid dynamics coupled to the global circulation in holistic setting: Mathematical models, numerical methods and applications

    Toro, Eleuterio Francisco | Celant, Morena | Zhang, Qinghui | Contarino, Christian | Agarwal, Nivedita | Linninger, Andreas | Müller, Lucas Omar

    International Journal for Numerical Methods in Biomedical Engineering, Vol. 38 (2022), Iss. 1

    https://doi.org/10.1002/cnm.3532 [Citations: 23]

  71. A high order approximation of hyperbolic conservation laws in networks: Application to one-dimensional blood flow

    Müller, Lucas O. | Blanco, Pablo J.

    Journal of Computational Physics, Vol. 300 (2015), Iss. P.423

    https://doi.org/10.1016/j.jcp.2015.07.056 [Citations: 39]

  72. Analysis of flow parameters of a Newtonian fluid through a cylindrical collapsible tube

    Kanyiri, Caroline W. | Kinyanjui, Mathew | Giterere, Kang’ethe

    SpringerPlus, Vol. 3 (2014), Iss. 1

    https://doi.org/10.1186/2193-1801-3-566 [Citations: 3]

  73. The Riemann Problem for the Blood Flow Model with Body Force Term

    Sheng, Wancheng | Xu, Shufang | Greco, Leopoldo

    Advances in Mathematical Physics, Vol. 2024 (2024), Iss. 1

    https://doi.org/10.1155/2024/2992241 [Citations: 0]