Kinetic discretization of one-dimensional nonlocal flow models

We show that one-dimensional nonlocal flow models in PDE form with Lighthill-Whitham-Richards flux supplemented appropriate in- and out-flow terms can be spatially discretized a finite volume scheme to obtain formally kinetic physically meaningful reaction graph structure. This allows the utilization of theory chemical networks, as demonstrated here via stability analysis model circular topology. further propose an explicit time discretization Courant-Friedrichs-Lewy condition ensuring many advantageous properties scheme. Additional characteristics, including monotonicity total variation diminishing property are also discussed.