Journal
TRANSPORTATION RESEARCH PART B-METHODOLOGICAL
Volume 35, Issue 4, Pages 337-365Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/S0191-2615(99)00054-5
Keywords
finite difference; Riemann problem; Godunov scheme; traffic flow
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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. (C) 2001 Elsevier Science Ltd. All rights reserved.
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