带有Chaplygin压力的耦合Aw-Rascle模型黎曼解的极限

翁莎莎; 潘丽君; 吕顺

doi:10.13568/j.cnki.651094.651316.2023.05.24.0002

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带有Chaplygin压力的耦合Aw-Rascle模型黎曼解的极限

更新时间：2026-01-21

- 带有Chaplygin压力的耦合Aw-Rascle模型黎曼解的极限
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 40, Issue 6, Pages: 683-690(2023)
- 作者机构：
  
  1. 南京航空航天大学数学学院
  2. 工业和信息化部飞行器数学建模和高性能计算重点实验室(NUAA)
- 作者简介：
- 基金信息：
- DOI：10.13568/j.cnki.651094.651316.2023.05.24.0002
  CLC： O186.12
- Published：2023
- 稿件说明：
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[1]翁莎莎,潘丽君,吕顺.带有Chaplygin压力的耦合Aw-Rascle模型黎曼解的极限[J].新疆大学学报(自然科学版)(中英文),2023,40(06):683-690.
[1]翁莎莎,潘丽君,吕顺.带有Chaplygin压力的耦合Aw-Rascle模型黎曼解的极限[J].新疆大学学报(自然科学版)(中英文),2023,40(06):683-690. DOI： 10.13568/j.cnki.651094.651316.2023.05.24.0002.

DOI：10.13568/j.cnki.651094.651316.2023.05.24.0002.

摘要

研究了带有Chaplygin压力的耦合Aw-Rascle(CAR)交通模型的黎曼问题.通过令耦合模型两侧压力同时消失，得到上述黎曼解的极限，并证明了该极限具有相同初值的无压气体动力（Pressureless Gas Dynamics

PGD）模型的黎曼解.更进一步，证得极限后的delta激波解的权重和速度与PGD模型的delta激波解的权重和速度完全一致.此外，由解的渐近行为，可以观察到稀疏接触间断到接触间断的转化.

Abstract

This paper considers the Riemann problem of the coupled Aw-Rascle(CAR) model with Chaplygin pressure. By letting the pressures on both sides of the CAR model vanish

the limits of the above Riemann solutions are obtained. Moreover

it is proved that the limits are the Riemann solutions to the pressureless gas dynamics(PGD) model with the same initial value. The weight and velocity of the delta shock after the limit are completely consistent with the weight and velocity of the delta shock to the PGD model. Furthermore

from the asymptotic behavior of the solutions

the transition from the rarefactive contact discontinuity to the contact discontinuity can be observed.

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references

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