The Riemann Problem for a Blood Flow Model in Arteries (Communications in Computational Physics, 2020)
In this paper, the Riemann solutions of a reduced 6×6 blood flow modelin medium-sized to large vessels are constructed. The model is non-strictly hyperbolicand non-conservative in nature, which brings two difficulties of the Riemann problem.One is the appearance of resonance while the other one is loss of uniqueness. Theelementary waves include shock wave, rarefaction wave, contact discontinuity andstationary wave. The stationary wave is obtained by solving a steady equation. Weconstruct the Riemann solutions especially when the steady equation has no solutionfor supersonic initial data. We also verify that the global entropy condition proposedby C.Dafermos can be used here to select the physical relevant solution. The Riemannsolutions may contribute to the design of numerical schemes, which can apply to thecomplex blood flows.