On the Riemann problem and interaction of elementary waves for two-layered blood flow model through arteries. (English) Zbl 1536.76155
Summary: In this paper, we focus on the Riemann problem for two-layered blood flow model, which is represented by a system of quasi-linear hyperbolic partial differential equations (PDEs) derived from the Euler equations by vertical averaging across each layer. We consider the Riemann problem with varying velocities and equal constant density through arteries. For instance, the flow layer close to the wall of vessel has a slower average speed than the layer far from the vessel because of the viscous effect of the blood vessel. We first establish the existence and uniqueness of the corresponding Riemann solution by a thorough investigation of the properties of elementary waves, namely, shock wave, rarefaction wave, and contact discontinuity wave. Further, we extensively analyze the elementary wave interaction between rarefaction wave and shock wave with contact discontinuity and rarefaction wave and shock wave. The global structure of the Riemann solutions after each wave interaction is explicitly constructed and graphically illustrated towards the end.
© 2023 John Wiley & Sons Ltd.
© 2023 John Wiley & Sons Ltd.
MSC:
| 76Z05 | Physiological flows |
| 92C35 | Physiological flow |
| 35L65 | Hyperbolic conservation laws |
| 35L67 | Shocks and singularities for hyperbolic equations |
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
Keywords:
elementary waves; exact solution; Riemann problem; two-layered blood flow model; wave interactionReferences:
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