The wave interactions of an improved Aw-Rascle-Zhang model with a non-genuinely nonlinear field

Abstract

<p style='text-indent:20px;'>This work is devoted to the study of the wave interactions of an improved Aw-Rascle-Zhang model with a non-genuinely nonlinear field. The wave interactions between single elementary waves involving the composite wave are analyzed by reviewing the Riemann solutions. Due to the non-genuinely nonlinear field, some new phenomena are found. The rarefaction waves may penetrate the shock waves. As a contact discontinuity interacts with the composite waves, there appear the compression waves which change to a contact discontinuity, then to rarefaction waves. Using the single wave interaction results, we construct the weak solutions of this model with three piecewise constant states. Finally, we give some intuitions to eliminate the "phantom traffic jam".</p>

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

“…Furthermore, Shao [40,41] established the existence and uniqueness of delta shock wave solution for the Riemann problem of traffic flow model and relativistic full Euler system. 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.…”