Intrinsic phenomena of delta shock waves in a more realistic Chaplygin Aw-Rascle model

TL;DR

This paper investigates delta shock waves in an enhanced Chaplygin Aw-Rascle model, deriving Riemann solutions with shock and rarefaction structures, and analyzing their convergence to delta shocks through theoretical and numerical methods.

Contribution

It introduces a more realistic Chaplygin gas version into the Aw-Rascle model and derives explicit Riemann solutions, including the convergence to delta shocks as pressure varies.

Findings

Riemann solutions with shock and rarefaction structures are established.

One solution converges to a delta-shock as pressure approaches the generalized Chaplygin gas pressure.

Numerical simulations validate the theoretical analysis.

Abstract

The motivation of this study is to find the Riemann solutions of the Aw-Rascle model with a more realistic version of extended Chaplygin gas. Firstly, we establish the Riemann solutions with two different structures, viz., a shock wave followed by the contact discontinuity and a rarefaction wave followed by the contact discontinuity. Further, by analyzing the limiting behavior, it is found that one of the Riemann solutions converges to a $ \delta $-shock solution as the pressure approaches the generalized Chaplygin gas pressure. Moreover, numerical simulations have been performed to validate the theoretical analysis.