Kinetic discretization of one-dimensional nonlocal flow models

2022. 03. 29. 16:00
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Vághy Mihály András (Pázmány Péter Catholic University)

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