Limits of solutions to the Aw-Rascle traffic flow model with generalized Chaplygin gas by flux approximation

Abstract

The Riemann problem for the Aw-Rascle (AR) traffic flow model with a double parameter perturbation containing flux and generalized Chaplygin gas is first solved. Then, we show that the delta-shock solution of the perturbed AR model converges to that of the original AR model as the flux perturbation vanishes alone. Particularly, it is proved that as the flux perturbation and pressure decrease, the classical solution of the perturbed system involving a shock wave and a contact discontinuity will first converge to a critical delta shock wave of the perturbed system itself and only later to the delta-shock solution of the pressureless gas dynamics (PGD) model. This formation mechanism is interesting and innovative in the study of the AR model. By contrast, any solution containing a rarefaction wave and a contact discontinuity tends to a two-contact-discontinuity solution of the PGD model, and the nonvacuum intermediate state in between tends to a vacuum state. Finally, some representatively numerical results consistent with the theoretical analysis are presented.