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Article Dans Une Revue Calcolo Année : 2021

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

Résumé

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.
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hal-03993025 , version 1 (28-02-2023)

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Alessia Del Grosso, Christophe Chalons. Second-order well-balanced Lagrange-projection schemes for blood flow equations. Calcolo, 2021, 58 (4), ⟨10.1007/s10092-021-00434-5⟩. ⟨hal-03993025⟩
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