Accepted Paper

Inserted: 22 jun 2019
Last Updated: 7 jun 2021

Journal: SIAM J. Num. An.
Year: 2020

Abstract:

We study a model of crowd motion following a gradient vector field, with possibly additional interaction terms such as attractionrepulsion, and we present a numerical scheme for its solution through a Lagrangian discretization. The density constraint of the resulting particles is enforced by means of a partial optimal transport problem at each time step. We prove the convergence of the discrete measures to a solution of the continuous PDE describing the crowd motion in dimension one. In a second part, we show how a similar approach can be used to construct a Lagrangian discretization of a linear advection-diffusion equation, interpreted as a gradient flow in Wasserstein space. We provide also a numerical implementation in 2D to demonstrate the feasibility of the computations.

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