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01-12-2021

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

Authors: A. Del Grosso, C. Chalons

Published in: Calcolo | Issue 4/2021

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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.

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Title: Second-order well-balanced Lagrange-projection schemes for blood flow equations
Authors: A. Del Grosso
C. Chalons
Publication date: 01-12-2021
Publisher: Springer International Publishing
Published in: Calcolo / Issue 4/2021
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI: https://doi.org/10.1007/s10092-021-00434-5

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

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