Approaching Chaplygin pressure limit of solutions to the Aw-Rascle model

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:416

Article

Cheng, Hongjun¹  Yang, Hanchun¹ 

[1] Yunnan Univ, Dept Math, Kunming 650091, Yunnan, Peoples R China

关键词: Aw-Rascle model;    Chaplygin gas;    Modified Chaplygin gas;    Delta-shocks;    Numerical simulations;   

DOI  :  10.1016/j.jmaa.2014.03.010

来源: Elsevier

【 摘 要 】

This paper studies the limit of solutions to the Aw-Ftascle model as the pressure tends to the Chaplygin gas pressure. For concreteness, the pressure is taken as a modified Chaplygin gas pressure. Firstly, the Riemann problem for the Aw-Rascle model with the modified Chaplygin gas pressure is solved constructively. Secondly, it is shown that as the pressure tends to the Chaplygin gas pressure, some Riemann solutions containing a shock and a contact discontinuity tend to a delta-shock solution, whose propagation speed and strength are different from those of deltashock solution to the Aw-Rascle model with a Chaplygin gas pressure. Besides, it is also proven that the rest Riemann solutions converge to a two-contact-discontinuity solution, which is exactly the solution to the Aw-Rascle model with a Chaplygin gas pressure. Thirdly, some numerical results are presented to exhibit the process of formation of delta-shocks. (C) 2014 Elsevier Inc. All rights reserved.

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