Modeling advection on distance-weighted directed networks
Michele Benzi, Fabio Durastante, Francesco Zigliotto · Mathematical Models and Methods in Applied Sciences · 2025
In this paper, we propose a model for describing advection dynamics on distance-weighted directed graphs. To this end we establish a set of key properties, or axioms, that a discrete advection operator should satisfy, and prove that there exists an essentially unique operator satisfying all such properties. Both infinite and finite networks are considered, as well as possible variants and extensions. We illustrate the proposed model through examples, both analytical and numerical, and we describe an application to the simulation of a traffic network.