The study of vehicular flow is vital for traffic optimization and urban planning. Traditionally, traffic models have been based on specific theories of vehicular behavior, but this paper proposes an innovative approach that utilizes the Navier–Stokes equations, which are classical in fluid dynamics, to model the flow of vehicles on roadways. We adapt these equations to capture the dynamics of vehicular traffic, treating vehicle movement as fluid flow rather than simple motion on a road. The approach relies on the analogy between fluid dynamics and traffic behavior, applying concepts of mass and momentum conservation to describe how vehicles cluster and disperse on a roadway. The necessary adaptations for viscosity and pressure in the context of vehicular traffic are examined, and simulations are presented to illustrate how this model can offer new perspectives on congestion and traffic flow. This work highlights the potential of the Navier–Stokes equations to provide a deeper understanding of traffic patterns and suggests new directions for future research in the optimization of vehicular flow and urban traffic management.

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Modeling Vehicular Flow Using an Approach Based on the Navier–Stokes Equations

  • Ernesto de la Cruz-Nicolás,
  • Hugo Estrada-Esquivel,
  • Alicia Martínez-Rebollar,
  • Odette Pliego-Martínez,
  • Eddie Clemente

摘要

The study of vehicular flow is vital for traffic optimization and urban planning. Traditionally, traffic models have been based on specific theories of vehicular behavior, but this paper proposes an innovative approach that utilizes the Navier–Stokes equations, which are classical in fluid dynamics, to model the flow of vehicles on roadways. We adapt these equations to capture the dynamics of vehicular traffic, treating vehicle movement as fluid flow rather than simple motion on a road. The approach relies on the analogy between fluid dynamics and traffic behavior, applying concepts of mass and momentum conservation to describe how vehicles cluster and disperse on a roadway. The necessary adaptations for viscosity and pressure in the context of vehicular traffic are examined, and simulations are presented to illustrate how this model can offer new perspectives on congestion and traffic flow. This work highlights the potential of the Navier–Stokes equations to provide a deeper understanding of traffic patterns and suggests new directions for future research in the optimization of vehicular flow and urban traffic management.