Flux approximation to the Aw-Rascle model of traffic flow
Flux approximation to the Aw-Rascle model of traffic flow
复制标题
交通流 Aw-Rascle 模型的通量近似
DOI：
10.1063/1.5063469
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发表时间：
2018-10
影响因子：
1.3
通讯作者：
Wanyi Xiao
中科院分区：
文献类型：
--
作者：
Jinjing Liu;Wanyi Xiao
本文分析了含压力的双参数通量近似下Aw-Rascle模型Riemann解的极限中的集中和空化现象以及增量激波和真空态的形成。证明了输运方程的解的极限趋向于特殊的增量激波，而不是经典的增量激波。为了进一步研究这个问题，我们考虑了一个扰动通量近似系统，并继续研究了解的极限。我们严格地证明了，当通量近似为零时，任何含有两个激波的黎曼解趋向于输运方程的增量激波；任何含有两个稀疏波的黎曼解趋于输运方程的双接触间断解，而介于两者之间的非真空中间态趋于真空态。此外，一些有代表性的数值模拟也证实了理论分析。在本文中，我们分析了包含压力的双参数通量近似的Aw-Rascle模型的Riemann解极限内的集中和空化现象以及增量激波和真空态的形成。证明了输运方程的解的极限趋向于特殊的增量激波，而不是经典的增量激波。为了进一步研究这个问题，我们考虑了一个扰动通量近似系统，并继续研究了解的极限。我们严格地证明了，当通量近似为零时，任何含有两个激波的黎曼解趋向于输运方程的增量激波；任何含有两个稀疏波的黎曼解趋于输运方程的双接触间断解，而介于两者之间的非真空中间态趋于真空态。此外，一些有代表性的数值模拟结果也证实了理论分析的正确性。
In this paper, we analyze the phenomena of concentration and cavitation and the formation of delta-shocks and vacuum states in the limit of Riemann solutions to the Aw-Rascle model with a two-parameter flux approximation including pressure. It is proved that the limit of solutions tends to a special delta-shock rather than the classical one to the transport equations. In order to further study this problem, we consider a perturbed flux approximation system and proceed to investigate the limits of solutions. We rigorously proved that, as the flux approximation vanishes, any Riemann solution containing two shock waves tends to a delta-shock to the transport equations; any Riemann solution containing two rarefaction waves tends to a two-contact-discontinuity solution to the transport equations and the nonvacuum intermediate state in between tends to a vacuum state. Moreover, some representative numerical simulations are exhibited to confirm the theoretical analysis.In this paper, we analyze the phenomena of concentration and cavitation and the formation of delta-shocks and vacuum states in the limit of Riemann solutions to the Aw-Rascle model with a two-parameter flux approximation including pressure. It is proved that the limit of solutions tends to a special delta-shock rather than the classical one to the transport equations. In order to further study this problem, we consider a perturbed flux approximation system and proceed to investigate the limits of solutions. We rigorously proved that, as the flux approximation vanishes, any Riemann solution containing two shock waves tends to a delta-shock to the transport equations; any Riemann solution containing two rarefaction waves tends to a two-contact-discontinuity solution to the transport equations and the nonvacuum intermediate state in between tends to a vacuum state. Moreover, some representative numerical simulations are exhibited to confirm the theoretical analysis.
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影响因子：
2.4
作者：
F. Huang;Zhen Wang
通讯作者：
F. Huang;Zhen Wang
影响因子：
6.8
作者：
H. M. Zhang
通讯作者：
H. M. Zhang
DOI：
10.1007/s11425-015-5034-0
发表时间：
2014-08
期刊：
Science China Mathematics
影响因子：
--
作者：
Hanchun Yang;Jinjing Liu
通讯作者：
Hanchun Yang;Jinjing Liu
影响因子：
1.3
作者：
Hanchun Yang;Jinhuan Wang
通讯作者：
Hanchun Yang;Jinhuan Wang
影响因子：
1.4
作者：
Yang Hanchun;Zhang Yu
通讯作者：
Zhang Yu