AN ENTROPY STABLE AND WELL-BALANCED SCHEME FOR AN AUGMENTED BLOOD FLOW MODEL WITH VARIABLE GEOMETRICAL AND MECHANICAL PROPERTIES

Raimund Bürger; Andrés Guerra; Carlos Vega

doi:10.29393/ppudec-16trrb30016

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Raimund Bürger Universidad de Concepción, Facultad de Ciencias Físicas y Matemática, Departamento de Ingeniería Matemática. Concepción, Chile.
Andrés Guerra Departamento de Matem´aticas y Estad´ıstica, Universidad del Norte, Km 5 via Puerto Colombia, Barranquilla, Colombia.
Carlos Vega Departamento de Matem´aticas y Estad´ıstica, Universidad del Norte, Km 5 vía Puerto Colombia, Barranquilla, Colombia.

DOI:

https://doi.org/10.29393/ppudec-16trrb30016

Keywords:

Augmented blood flow model, vessel with variable properties, well-balanced scheme, entropy stable scheme

Resumen

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.

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