Riemann problems for the nonhomogeneous Aw-Rascle model

In this paper the celebrated second order Aw-Rascle nonhomogeneous system describing traffic flows is considered. Within the framework of the method of differential con-straints, a suitable reduction procedure is developed for solving a class of Riemann problems which are of interest in traffic flows theory. In particular, for a given source term, we find the general solution of the Riemann problem in terms of shock waves, contact discontinuities and generalized rarefaction waves. The interaction between a shock wave and a generalized rarefaction wave is also studied and a related generalized Riemann problem is solved. Numerical results are in agreement with the exact analytical solution. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper examines the well-known second order Aw-Rascle nonhomogeneous system that describes traffic flows. Using the method of differential constraints, a suitable reduction procedure is developed to solve a class of Riemann problems in traffic flow theory. The general solution of the Riemann problem, including shock waves, contact discontinuities, and generalized rarefaction waves, is obtained for a given source term. The interaction between a shock wave and a generalized rarefaction wave is also studied, and a related generalized Riemann problem is solved. Numerical results agree with the exact analytical solution.