VILLADA , Luis Miguel

We extend the finite volume numerical scheme proposed by Hilliges and Weidlich [11] to second order traffic flow models consisting in 2 × 2 systems of non strictly hyperbolic conservation laws of Temple class. The scheme is shown to satisfy some maximum principle properties on the density. We provide numerical tests illustrating the behaviour...

We propose a nonlocal macroscopic pedestrian flow model for two populations with different destinations trying to avoid each other in a confined environment, where the nonlocal term accounts for anisotropic interactions, mimicking the effect of different cones of view, and the presence of walls or other obstacles in the domain. In particular,...

We propose three variants of a nonlocal macroscopic pedestrian flow model accounting for anisotropic interactions between different groups and including the presence of walls or other obstacles in the walking domain. We compare the solutions behaviour in the case of bi-directional flows and othogonally crossing flows by numerical simulation...

This paper focuses on the numerical approximation of the solutions of nonlocal conservation laws in one space dimension. These equations are motivated by two distinct applications, namely, a traffic flow model in which the mean velocity depends on a weighted mean of the downstream traffic density, and a sedimentation model where either the...

This paper focuses on the numerical approximation of a class of non-local systems of conservation laws in one space dimension, arising in traffic modeling, proposed by [F. A. Chiarello and P. Goatin. Non-local multi-class traffic flow models. Networks and Heterogeneous Media, to appear, Aug. 2018]. We present the multi-class version of the...

This paper focuses on the numerical approximation of the solutions of a class of non-local systems in one space dimension, arising in traffic modeling. We propose alternative simple schemes by splitting the non-local conservation laws into two different equations, namely, the Lagrangian and the remap steps. We provide some properties and...

This study revises the non-local macroscopic pedestrian flow model proposed in [R. M. Colombo, M. Garavello, and M. Lécureux-Mercier. A class of nonlocal models for pedestrian tra c. Math. Models Methods Appl. Sci., 22(4):1150023, 34, 2012] to account for anisotropic interactions and the presence of walls or other obstacles in the walking...