Numerical Solution of Homogeneous Aw-Rascle Type Traffic Flow Models Using an Improved Wave Propagation-HLLE Approach

Abstract

Homogeneous second-order Aw-Rascle-type models have demonstrated greater effectiveness than their non-homogeneous counterparts in traffic flow modeling. This study addresses the numerical solution of hyperbolic conservation laws governing these models by coupling the second-order HLLE Riemann solver, a Godunov-type finite volume approach, with the wave propagation algorithm. A novel wave-speed selection strategy is proposed by comparing characteristic velocities with Roe speeds, yielding solutions with guaranteed positive density and speed. The proposed IWPHLLE method is applied to simulate shock, rarefaction, and contact discontinuity waves under homogeneous long-road conditions, eliminating the influence of external source terms and ensuring the homogeneity of the governing hyperbolic equations. Its performance is benchmarked against the MacCormack scheme supplemented by two standard stabilization techniques, namely artificial viscosity (AV) and central differencing (CD). Spatiotemporal distributions and density profiles are examined across four representative traffic scenarios: free flow, congested traffic flow, queue dissolution, and congested flow with non-equilibrium velocity and uniform density. The results demonstrate that the IWP-HLLE approach substantially suppresses numerical oscillations compared to both AV and CD methods while maintaining stability across all test cases.