Numerical research of the mathematical model for traffic flow

A. S. Konkina

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 4, pp. 128-134

Résumé

The problems of distribution of transport flows are currently relevant in connection with the increase in vehicles. In the 50s of the last century, the first macroscopic (hydrodynamic) models appeared, where the transport flow resembles the flow “motivated” compressible liquid. The scientific approach based on the Navier–Stokes system. The main idea of the scholars is consideration the hydrodynamic models on the grounds of interrelation between the transport flow and incompressible fluid. For modelling traffic flows we examine Oskolkov equation on the geometric graph, where the edge has two positive values corresponding to it “length” and “width”. Certainly, in the context of mathematical model the values $l_{k}$ and $b_{k}$ are dimensionless, but for clarity it is convenient to imagine that $l_{k}$ is measured in linear metric units, for example, kilometers or miles, and $b_{k}$ is equal to the number of traffic lanes on the roadway in one direction. In terms of the Oskolkov model, we obtained a non-classical multipoint initial-final value condition. We will study such a model using the idea and methods of the Sobolean equation theory. These notes describe a numerical experiment based on the Galerkin method for the Oskolkov equation with a multipoint initial-final condition on the graph.

Détail

Keywords: Oskolkov equation, geometric graph, multipoint initial-final condition, traffic flows.