Riemann problem and Godunov-type scheme for a two-layer blood flow model

Abstract

We establish and investigate a two-layer blood flow model with two velocities in this paper. The mass exchange of the flows and the acceleration offset term between each layer have been incorporated into the model as source terms. We derive the elementary waves and solve the Riemann problem constructively. Besides, we develop a Godunov scheme for the new model. Numerical simulations are given to verify the effective and versatility of the model. The results may contribute to the application in more layers blood flow and the design of high order numerical schemes.