Abstract
We generalize the results on conservation laws with local flux constraint obtained in [1, 9] to general flux functions and nonclassical solutions arising for example in pedestrian flow modeling. We first define the constrained Riemann solver and the entropy condition, which singles out the unique admissible solution. We provide a well posedness result based on wave-front tracking approximations and Kruzhkov doubling of variable technique. We then provide the framework to deal with nonclassical solutions and we propose a front-tracking finite volume scheme allowing to sharply capture classical and nonclassical discontinuities. Numerical simulations illustrating the Braess paradox are presented as validation of the method.
Highlights
Several phenomena displayed by vehicular traffic can be modeled using conservation laws in one space-dimension, see for example [18] for a survey of available models
Colombo and Rosini [12] introduced a model for pedestrian flow accounting for panic appearance and consisting in a scalar conservation law in one space-dimension displaying nonclassical shocks
In [13] the authors show that the flux constraint represented by the presence of a door may cause the onset of panic states from a normal situation
Summary
Several phenomena displayed by vehicular traffic can be modeled using conservation laws in one space-dimension, see for example [18] for a survey of available models. Colombo and Rosini [12] introduced a model for pedestrian flow accounting for panic appearance and consisting in a scalar conservation law in one space-dimension displaying nonclassical shocks Such a simplified model can be used for example to describe the motion of a crowd along a corridor or a bridge. In [13] the authors show that the flux constraint represented by the presence of a door may cause the onset of panic states from a normal situation In this model, the flux function is not concave (nor convex) and it does not match the available results about conservation laws with constrained flux.
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