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An entropy stable and well-balanced scheme for an augmented blood flow model with variable geometrical and mechanical properties

Author

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  • Bürger, Raimund
  • Guerra, Andrés
  • Vega, Carlos A.

Abstract

The flow of blood through a vessel can be described by a hyperbolic system of balance equations for the cross-sectional area and averaged velocity as functions of axial spatial position and time. The variable arterial wall rigidity and the equilibrium cross-sectional area are incorporated within the so-called tube law that gives rise to an internal pressure term. This system can be written as a conservative hyperbolic system for five unknowns. An entropy stable scheme for this augmented one-dimensional blood flow model is developed based on entropy conservative numerical flux. It is proved that the proposed scheme is well-balanced in the sense that it preserves both trivial (zero velocity) and non-trivial (non-zero velocity) steady-state solutions. Several demanding numerical tests show that the scheme can handle various kinds of shocks and preserves stationary solutions when geometrical and mechanical properties of the vessel are variable.

Suggested Citation

  • Bürger, Raimund & Guerra, Andrés & Vega, Carlos A., 2026. "An entropy stable and well-balanced scheme for an augmented blood flow model with variable geometrical and mechanical properties," Applied Mathematics and Computation, Elsevier, vol. 510(C).
    • Handle: RePEc:eee:apmaco:v:510:y:2026:i:c:s009630032500445x
    DOI: 10.1016/j.amc.2025.129719
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    References listed on IDEAS

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    1. Xiaofei Wang & Jose-Maria Fullana & Pierre-Yves Lagrée, 2015. "Verification and comparison of four numerical schemes for a 1D viscoelastic blood flow model," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 18(15), pages 1704-1725, November.
    2. Pandey, Prashant Kumar & Dubey, Ritesh Kumar, 2023. "Sign stable arbitrary high order reconstructions for constructing non-oscillatory entropy stable schemes," Applied Mathematics and Computation, Elsevier, vol. 454(C).
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