The Interaction of Waves in the Zero-Pressure Euler Equations with a Coulomb-Like Friction Term

Wang, Aiju; Yu, Wangxun; Zhang, Yanyan

doi:10.1155/2022/4837968

Cited by 2 publications

(1 citation statement)

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“…The results of single‐wave interaction have been used by Jiang et al [42] to derive the weak solution for the Aw–Rascle–Zhang model with a non‐genuinely nonlinear field, and their investigation gives a relief from the traffic congestion. Wang et al [43] presented the interaction among contact discontinuity, vacuum, and delta shock for the Euler equations without pressure with a Coulomb‐like friction term. Chaudhary and Singh [44] explored all possible elementary wave interactions of dusty gas flow.…”

Section: Introductionmentioning

confidence: 99%

On the Riemann problem and interaction of elementary waves for two‐layered blood flow model through arteries

Jana,

Kuila

2023

Math Methods in App Sciences

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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.

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Section: Introductionmentioning

confidence: 99%