We consider the 1D blood flow equations with friction source term. The main purpose of this work is the derivation of a positivity preserving and fully well-balanced scheme, which correctly approximates the solutions of this system, exactly preserves all the associated steady states, including the moving ones, and ensures the positivity of the cross-sectional area. To address such issues, a study of the moving steady states related to the friction source term is first performed. Afterwards, a Godunov-type scheme is constructed, by deriving a two-state approximate Riemann solver and by introducing a relevant discretization of the source term, to enforce the well-balanced property. The scheme is then adapted to the generalized model including a space-variable viscous resistance; a second-order well-balanced MUSCL extension of the scheme is also proposed. Numerical experiments are finally carried out in order to validate the scheme and highlight its properties.

A Fully Well-balanced Scheme for the 1D Blood Flow Equations with Friction Source Term / Ghitti, B.; Berthon, C.; Le, M. H.; Toro, E. F.. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - 2020, 421:109750(2020), pp. 1-33. [10.1016/j.jcp.2020.109750]

A Fully Well-balanced Scheme for the 1D Blood Flow Equations with Friction Source Term

Ghitti B.;Toro E. F.
2020-01-01

Abstract

We consider the 1D blood flow equations with friction source term. The main purpose of this work is the derivation of a positivity preserving and fully well-balanced scheme, which correctly approximates the solutions of this system, exactly preserves all the associated steady states, including the moving ones, and ensures the positivity of the cross-sectional area. To address such issues, a study of the moving steady states related to the friction source term is first performed. Afterwards, a Godunov-type scheme is constructed, by deriving a two-state approximate Riemann solver and by introducing a relevant discretization of the source term, to enforce the well-balanced property. The scheme is then adapted to the generalized model including a space-variable viscous resistance; a second-order well-balanced MUSCL extension of the scheme is also proposed. Numerical experiments are finally carried out in order to validate the scheme and highlight its properties.
2020
109750
Ghitti, B.; Berthon, C.; Le, M. H.; Toro, E. F.
A Fully Well-balanced Scheme for the 1D Blood Flow Equations with Friction Source Term / Ghitti, B.; Berthon, C.; Le, M. H.; Toro, E. F.. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - 2020, 421:109750(2020), pp. 1-33. [10.1016/j.jcp.2020.109750]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/331872
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