Riemann solutions of the anti-Chaplygin pressure Aw–Rascle model with friction

Abstract

The Riemann problem for the anti-Chaplygin pressure Aw–Rascle model with a Coulomb-like friction term is considered. With the use of the substitution of variables, the Riemann solutions with two or three kinds of different structures involving the delta shock wave in two cases are constructed. The delta shock wave may be used to explain the serious traffic jam. The position, strength, and propagation speed of the delta shock wave are obtained by solving the generalized Rankine–Hugoniot relation under an entropy condition. Moreover, the results show that all waves including the contact discontinuity, rarefaction wave, shock wave, and delta shock wave are bent into parabolic shapes and the Riemann solutions are no longer self-similar under the influence of the Coulomb-like friction term.