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.
Jannelli A., Manganaro N., Rizzo A. (2023). Riemann problems for the nonhomogeneous Aw-Rascle model. COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION, 118 [10.1016/j.cnsns.2022.107010].
Riemann problems for the nonhomogeneous Aw-Rascle model
Rizzo A.
2023-04-01
Abstract
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.File | Dimensione | Formato | |
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