  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.
