High-resolution numerical approximation of traffic flow problems with variable lanes and free-flow velocities

This paper develops macroscopic traffic flow models for a highway section with variable lanes and free-flow velocities, that involve spatially varying flux functions. To address this complex physical property, we develop a Riemann solver that derives the exact flux values at the interface of the Riemann problem. Based on this solver, we formulate Godunov-type numerical schemes to solve the traffic flow models. Numerical examples that simulate the traffic flow around a bottleneck that arises from a drop in traffic capacity on the highway section are given to illustrate the efficiency of these schemes.