A Steady-State-Preserving Numerical Scheme for One-Dimensional Blood Flow Model

Carlos A. Vega (), Sonia Valbuena and Jesús Blanco Bojato
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Carlos A. Vega: Departamento de Matemáticas y Estadística, Universidad del Norte, Barranquilla 080001, Colombia
Sonia Valbuena: Grupo de Investigación GIMED, Universidad del Atlántico, Barranquilla 080001, Colombia
Jesús Blanco Bojato: Departamento de Matemáticas y Estadística, Universidad del Norte, Barranquilla 080001, Colombia

Mathematics, 2024, vol. 12, issue 3, 1-12

Abstract: In this work, an entropy-stable and well-balanced numerical scheme for a one-dimensional blood flow model is presented. Such a scheme was obtained from an explicit entropy-conservative flux along with a second-order discretisation of the source term by using centred finite differences. We prove that the scheme is entropy-stable and preserves steady-state solutions. In addition, some numerical examples are included to test the performance of the proposed scheme.

Keywords: one-dimensional blood flow model; balanced laws; entropy-stable scheme; steady-states (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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