A finite difference method with adaptive time mesh for hyperbolic traffic flow

Abstract

This paper presents a finite difference method with variable time mesh for the hyperbolic traffic flow. The width of each time step is determined by the ratio of uniform space mesh size and maximal characteristic velocity. The proposed adaptive time mesh scheme Is compatible with most of explicit finite difference methods. Numerical examples with different initial and boundary conditions of the Lighthill-Whitham-Richards (LWR) model and Payne-Whitham model are provided to contrast the effects of adaptive time mesh on the Lax-Friedrichs scheme. Simulation results are generally satisfied. The number of time steps of adaptive-Lax method is much less than that of Lax method with no significant difference in solutions of LWR model. Convergence of solution is readily claimed by the Courant-Friedrichs-Lewy (CFL) condition.