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

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