High-order fully well-balanced numerical methods for one-dimensional blood flow with discontinuous properties

Abstract

In this paper, we are interested in the numerical study of the one-dimensional blood flow model with discontinuous mechanical and geometrical properties. We present the mathematical model together with its nondimensional form. We do an exhaustive investigation of all its stationary solutions and we propose high-order fully well-balanced numerical methods that are able to preserve all of them. They are based on the combination of the Generalized Hydrostatic Reconstruction and well-balanced reconstruction operators. These methods are able to deal with more than one discontinuous parameter. Several numerical tests are shown to prove its well-balanced and high-order properties, and its convergence to the exact solutions.