The limiting behavior of Riemann solutions to the hydrodynamic Aw-Rascle traffic model

Abstract

The hydrodynamic Aw-Rascle traffic model is proposed by combining the Aw-Rascle model and the pressureless hydrodynamic model, whose Riemann solutions are solved explicitly based on the fine analysis of elementary waves. As the traffic pressure vanishes, the asymptotic behavior of Riemann solutions is analyzed carefully, in which the intrinsic nonlinear phenomena of concentration and cavitation are observed and explored. Moreover, it is found interestingly that the vanishing traffic pressure limit of the Riemann solution for the hydrodynamic Aw-Rascle traffic model is different obviously from the one for the pressureless hydrodynamic model under the specially designated circumstance due to the different choices of the over-compressive entropy conditions of delta shock wave.