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

This paper studies the limit of solutions to the Aw–Rascle 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...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 416; no. 2; pp. 839 - 854
Main Authors Cheng, Hongjun, Yang, Hanchun
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.08.2014
Subjects
Aw–Rascle model
Chaplygin gas
Delta-shocks
Modified Chaplygin gas
Numerical simulations
Modified Chaplygin gas
Aw–Rascle model
Numerical simulations
Delta-shocks
Chaplygin gas
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Summary:This paper studies the limit of solutions to the Aw–Rascle 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 delta-shock 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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2014.03.010