具复合压力项的Aw-Rascle交通流模型的Riemann问题及其奇异极限研究  

The Riemann Problem for the Aw-Rascle Traffic Flow Model with a Composite Pressure Term and Its Singular Limit

作　　者：张庆玲 刘星宇 董娜 ZHANG Qingling;LIU Xingyu;DONG Na(School of Artificial Intelligence,Jianghan University,Wuhan 430056,Hubei,China)

机构地区：[1]江汉大学人工智能学院,湖北武汉430056

出　　处：《江汉大学学报（自然科学版）》2023年第1期10-17,共8页Journal of Jianghan University：Natural Science Edition

基　　金：湖北省大学生创新创业训练计划项目(S202111072045);江汉大学校级科研项目(2021yb059)。

摘　　要：研究了具复合压力项的Aw-Rascle交通流模型的Riemann问题。首先,运用特征分析法,计算出Aw-Rascle交通流模型的特征值、特征向量和对应的基本波曲线;然后,利用相平面分析法,给出所有情形下对应的Riemann解;最后,讨论了当压力消失时Riemann解的极限行为,并详细研究了压力消失过程中δ-激波和真空状态的形成。This paper studied the Riemann problem for the Aw-Rascle traffic flow model with a composite pressure term.First,using the characteristic analysis method,we calculated the eigenvalues,eigenvectors,and corresponding fundamental wave curves of the AwRascle traffic flow model.Then,using the phase plane analysis method,the corresponding Riemann solutions for all cases were given.Finally,we discussed the limiting behavior of the Riemann solution when the pressure disappeared,and studied the formation of theδ-shock wave and vacuum state during the process of pressure disappearance.

关 键 词：Aw-Rascle交通流 RIEMANN问题 δ-激波 真空状态 奇异极限 

分 类 号：O175.27[理学—数学]