修正Chaplygin气体情形下AW-Rascle模型的Riemann问题及基本波的相互作用

Riemann problem and interaction of elementary waves of modified Chaplygin AW-Rascle model

研究了一维修正Chaplygin气体AW-Rascle模型的Riemann解及基本波的相互作用.利用特征分析法和相平面分析法,由Rankine-Hugoniot条件和熵条件,构造性地得到了解的存在性和解的整体结构,Riemann解由R+J或S+J组成.利用Riemann解的结论,分情况讨论了4种基本波的相互作用:R+J和S+J;S+J和S+J;S+J和R+J;R+J和R+J.最后,令扰动参数趋于零,证明了Riemann解的稳定性.

This paper considered the Riemann solution and the interaction of elementary waves for the traffic flow model proposed with the modified Chaplygin gas pressure law.Firstly,under the Rankine-Hugoniot relation and the entropy condition,the global Riemann solution was constructively obtained by the characteristic and phase plane analysis.The Riemann solution consists of R+J or S+J according to the different data ranges of the initial data.Furthermore,with these results of Riemann problem,four cases were discussed according to the different combinations of elementary waves as following:R+J and S+J,S+J and S+J,S+J and R+J,R+J and R+J,when the initial data consist of three pieces of constant states.Finally,let the perturbed parameter tend to zero,the stability of the Riemann solutions was proved.