## Journals

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### Open Access Journals

NHM

This paper is devoted to the study of the one dimensional interfacial coupling of two PDE systems at
a given fixed interface, say $x=0$. Each system is posed on a half-space, namely $x<0$
and $x>0$. As an interfacial model, a coupling condition whose objective is to enforce
the continuity (in a weak sense) of a prescribed variable is generally imposed at $x=0$.

We first focus on the coupling of two scalar conservation laws and state an existence result for the coupled Riemann problem. Numerical experiments are also proposed. We then consider, both from a theoretical and a numerical point of view, the coupling of two-phase flow models namely a drift-flux model and a two-fluid model. In particular, the link between both models will be addressed using asymptotic expansions.

We first focus on the coupling of two scalar conservation laws and state an existence result for the coupled Riemann problem. Numerical experiments are also proposed. We then consider, both from a theoretical and a numerical point of view, the coupling of two-phase flow models namely a drift-flux model and a two-fluid model. In particular, the link between both models will be addressed using asymptotic expansions.

NHM

We extend the results on conservation laws with local flux constraint
obtained in [2, 12] to general (non-concave) flux functions and non-classical solutions
arising in pedestrian flow modeling [15].
We first provide a well-posedness result based on wave-front tracking approximations and the Kružhkov
doubling of variable technique for a general conservation law with constrained flux.
This provides a sound basis for dealing with non-classical solutions accounting for panic states
in the pedestrian flow model introduced by Colombo and Rosini [15].
In particular, flux constraints are used here to model the presence of doors and obstacles.
We propose a "front-tracking" finite volume scheme allowing to sharply capture classical and non-classical
discontinuities. Numerical simulations illustrating the Braess paradox are presented as validation of the method.

DCDS-B

We introduce a second order model for traffic flow with moving bottlenecks. The model consists of the × 2$ Aw-Rascle-Zhang system with a point-wise flow constraint whose trajectory is governed by an ordinary differential equation. We define two Riemann solvers, characterize the corresponding invariant domains and propose numerical strategies, which are effective in capturing the non-classical shocks due to the constraint activation.

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