General constrained conservation laws. Application to pedestrian flow modeling.

Christophe Chalons (1, 2) , Paola Goatin (3) , Nicolas Seguin (1, 4)

1 LJLL - Laboratoire Jacques-Louis Lions
2 UPD7 - Université Paris Diderot - Paris 7
3 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
4 UPMC - Université Pierre et Marie Curie - Paris 6

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.

Domaines: Equations aux dérivées partielles [math.AP]

Christophe Chalons, Paola Goatin, Nicolas Seguin. General constrained conservation laws. Application to pedestrian flow modeling.. Networks and Heterogeneous Media, 2013, 8 (2), pp.433-463. ⟨hal-00713609⟩