Lagrangian Discretization Of Crowd Motion And Linear Diffusion

We study a model of crowd motion following a gradient vector field, with possibly additional interaction terms such as attraction/repulsion, 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. Both discretizations rely on the interpretation of the two equations (crowd motion and linear diffusion) as gradient flows in Wasserstein space. We provide also a numerical implementation in 2 dimensions to demonstrate the feasibility of the computations.


Published in:
Siam Journal On Numerical Analysis, 58, 4, 2093-2118
Year:
Jan 01 2020
Publisher:
Philadelphia, SIAM PUBLICATIONS
ISSN:
0036-1429
1095-7170
Keywords:




 Record created 2020-09-26, last modified 2020-10-29


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