A finite difference approximation of a non-equilibrium traffic flow model

We develop in this paper a finite difference scheme for a previously reported non-equilibrium traffic flow model. This scheme is an extension of Godunov's scheme to systems. It utilizes the solutions of a series of Riemann problems at cell boundaries to construct approximate solutions of the non-equilibrium traffic flow model under general initial conditions. Moreover, the Riemann solutions at both left (upstream) and right (downstream) boundaries of a highway allow the specification of correct boundary conditions using state variables (e.g., density and/or speed) rather than fluxes. Preliminary numerical results indicate that the finite difference scheme correctly computes entropy-satisfying weak solutions of the original model.