THE WAVE INTERACTIONS OF AN IMPROVED AW-RASCLE-ZHANG MODEL WITH A NON-GENUINELY NONLINEAR FIELD

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.

Automated summary

This study focuses on the wave interactions of an improved Aw-Rascle-Zhang model with a non-genuinely nonlinear field. By analyzing the Riemann solutions, the wave interactions between single elementary waves involving the composite wave are examined. The presence of a non-genuinely nonlinear field leads to the discovery of new phenomena, such as the ability of rarefaction waves to penetrate shock waves and the transformation of compression waves to rarefaction waves during the interaction with a contact discontinuity. Furthermore, the weak solutions of this model with three piecewise constant states are constructed based on the results of single wave interactions, providing insights for eliminating phantom traffic jams.