Point constriction, interface, and boundary conditions for kinematic-wave model

Abstract

The entropy solutions of the Riemann problem for the kinematic-wave model are described for (entrant and exiting) boundary conditions, interfaces (e.g., lane drops), and point constrictions (e.g., bottlenecks or signalized intersections) for kinematic-wave models. These results are used to obtain analytic solutions and computational solutions, by the method of Godunov, for the three test scenarios earlier suggested by Ross. Results show that the kinematic-wave model, with a correct computational solution (i.e., converging to the entropy solution), correctly produces the analytic (entropy) solutions of the kinematic-wave model and that analytic and computational solutions both satisfy intuitive expectations at least as well as the novel model suggested by Ross and even avoid some acknowledged deficiencies of the latter. They also emphasize the necessity of using discrete approximations that satisfy the entropy condition and of exercising care in ensuring that the discretization parameters are sufficiently small.