Modeling advection on distance-weighted directed networks

TL;DR

This paper introduces a novel model for simulating advection processes on distance-weighted directed networks, establishing key axioms and demonstrating its applicability through analytical, numerical, and traffic network examples.

Contribution

It defines a set of axioms for discrete advection operators and proves the existence of a unique operator satisfying these properties, extending to various network types.

Findings

Existence of a unique advection operator satisfying key axioms

Application demonstrated on traffic network simulations

Model applicable to both finite and infinite networks

Abstract

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.