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

We focus on the development of well-balanced Lagrange-projection schemes applied to the one-dimensional blood flow system of balance laws. Here we neglect the friction forces and the source term is due to the presence of varying parameters as the cross-sectional area at the equilibrium and the arter...

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Published in:	Calcolo Vol. 58; no. 4
Main Authors:	Del Grosso, A., Chalons, C.
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01-12-2021 Springer Nature B.V Springer Verlag
Subjects:	Blood flow Flow equations Mathematics Mathematics and Statistics Numerical Analysis Riemann solver Stiffness Theory of Computation Blood flow equations Well-balanced property Second-order of accuracy Lagrange-projection splitting 65M08 Approximate Riemann solver
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Abstract	We focus on the development of well-balanced Lagrange-projection schemes applied to the one-dimensional blood flow system of balance laws. Here we neglect the friction forces and the source term is due to the presence of varying parameters as the cross-sectional area at the equilibrium and the arterial stiffness. By well-balanced we mean that the method preserves the “man at eternal rest” solution. For this purpose we present two different strategies: the former requires a consistent definition of the source term based on an approximate Riemann solver, while the second one exploits the well-established hydrostatic reconstruction. Subsequently we explain how to reach the second-order of accuracy for both procedures. Numerical simulations are carried out in order to show the right order of accuracy and the good behaviour of the schemes.
AbstractList	We focus on the development of well-balanced Lagrange-projection schemes applied to the one-dimensional blood flow system of balance laws. Here we neglect the friction forces and the source term is due to the presence of varying parameters as the cross-sectional area at the equilibrium and the arterial stiffness. By well-balanced we mean that the method preserves the “man at eternal rest” solution. For this purpose we present two different strategies: the former requires a consistent definition of the source term based on an approximate Riemann solver, while the second one exploits the well-established hydrostatic reconstruction. Subsequently we explain how to reach the second-order of accuracy for both procedures. Numerical simulations are carried out in order to show the right order of accuracy and the good behaviour of the schemes.
ArticleNumber	43
Author	Chalons, C. Del Grosso, A.
Author_xml	– sequence: 1 givenname: A. orcidid: 0000-0001-9191-8156 surname: Del Grosso fullname: Del Grosso, A. email: alessia.del-grosso@ens.uvsq.fr organization: Laboratoire de Mathématiques de Versailles, UMR 8100, Université de Versailles Saint-Quentin-en-Yvelines, UFR des Sciences, bâtiment Fermat – sequence: 2 givenname: C. surname: Chalons fullname: Chalons, C. organization: Laboratoire de Mathématiques de Versailles, UMR 8100, Université de Versailles Saint-Quentin-en-Yvelines, UFR des Sciences, bâtiment Fermat
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Keywords	Blood flow equations Well-balanced property Second-order of accuracy Lagrange-projection splitting 65M08 Approximate Riemann solver
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Harten (434_CR32) 1983; 25 434_CR9 MJ Castro (434_CR11) 2020; 82 T Morales De Luna (434_CR23) 2020; 18 V Michel-Dansac (434_CR14) 2016; 72 V Michel-Dansac (434_CR15) 2017; 335 F Duboc (434_CR28) 2010; 348 LO Müller (434_CR16) 2013; 242 EF Toro (434_CR7) 2013; 13 I Suliciu (434_CR24) 1998; 36 Zhenzhen Wang (434_CR5) 2016 L Formaggia (434_CR1) 2009 434_CR21 C Chalons (434_CR19) 2017; 335 434_CR2 434_CR3 G Gallice (434_CR25) 2002; 334 C Chalons (434_CR18) 2013 EF Toro (434_CR27) 2016; 272 AR Ghigo (434_CR4) 2017; 331 F Bouchut (434_CR8) 2004 G Gallice (434_CR26) 2003; 94 LO Müller (434_CR17) 2013; 29
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Snippet	We focus on the development of well-balanced Lagrange-projection schemes applied to the one-dimensional blood flow system of balance laws. Here we neglect the...
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SubjectTerms	Blood flow Flow equations Mathematics Mathematics and Statistics Numerical Analysis Riemann solver Stiffness Theory of Computation
Title	Second-order well-balanced Lagrange-projection schemes for blood flow equations
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