Finite Volume Method for a System of Continuity Equations Driven by Nonlocal Interactions
Analysis of PDEs
2019-12-16 v1
Abstract
We present a new finite volume method for computing numerical approximations of a system of nonlocal transport equation modeling interacting species. This method is based on the work [F. Delarue, F. Lagoutire, N. Vauchelet, Convergence analysis of upwind type schemes for the aggregation equation with pointy potential, Ann. Henri. Lebesgue 2019], where the nonlocal continuity equations are 10 treated as conservative transport equations with a nonlocal, nonlinear, rough velocity field. We analyze some properties of the method, and illustrate the results with numerical simulations.
Keywords
Cite
@article{arxiv.1912.06423,
title = {Finite Volume Method for a System of Continuity Equations Driven by Nonlocal Interactions},
author = {Anissa Keurti and Thomas Rey},
journal= {arXiv preprint arXiv:1912.06423},
year = {2019}
}
Comments
8 pages, 2 figures