Riemann problem for Aw-Rascle model with more realistic version of extended Chaplygin gas

Abstract: The motivation of this study is to find the Riemann solutions of Aw-Rascle model with friction for a more realistic version of extended Chaplygin gas. Firstly, we established the $ \delta $-shock wave in its solutions; indeed, by using generalized Rankine Hugoniot jump conditions the position, strength, and velocity of $ \delta $-shock are obtained. Further, by analyzing the limiting behavior, it is found that one of the Riemann solutions converges to $ \delta $-shock solution as the pressure approaches to generalized Chaplygin gas pressure. Moreover, we obtained that our Riemann solutions converge to the corresponding solutions of the transport equations as pressure tends to zero. Furthermore, we explicitly construct the Riemann solutions of the inhomogeneous Aw-Rascle model.