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

• 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
• ISSN: 0008-0624; 1126-5434
• DOI: 10.1007/s10092-021-00434-5

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.