Finite volume method for simulations of traffic dynamics with exits and entrances

Abstract

We discuss a macroscopic study of vehicle traffic dynamics in which traffic flow is considered as a continuum governed by the kinematic Lighthill--Whitham--Richard model, with a source term accounting for traffic entries and exits through a junction. The kinematic model is solved using finite volume method, with the flux function is approximated using the upwind method. In order to prevent flows which exceed road capacity and to preserve the positivity of traffic density in simulations with entries and exits, a stop-go procedure is adopted. The resulting scheme is used to simulate the responses of traffic density to light and heavy entrances from a junction, and the dynamics predicted by the simulations are shown to conform well to analytical solutions. With a validated numerical algorithm at hand, we simulate traffic dynamics for several scenarios on a roadway with entrances and exits. Depending on the rate of exit or entrance and the initial condition, density profiles in the form of shock wave and rarefaction wave may appear. References

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