Revista UIS Ingenierías

Vol. 22 No. 2 (2023): Revista UIS Ingenierías
Articles

Solution of the traffic flow equation using the finite element method

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  • Fernando Mesa,
  • Diana Devia-Narváez ,
  • Rogelio Ospina-Ospina
Fernando Mesa
Universidad Tecnológica de Pereira
Diana Devia-Narváez
Universidad Tecnológica de Pereira
Rogelio Ospina-Ospina
Universidad Industrial de Santander
DOI: https://doi.org/10.18273/revuin.v22n2-2023006

Published 2023-04-07

Keywords

  • combination linear,
  • Dirichlet conditions,
  • Neumann conditions,
  • Robin conditions,
  • contour,
  • partial differential equation,
  • traffic Flow,
  • positive semidefinite matrix,
  • finite element method,
  • numerical solution,
  • tridiagonal
    • ...More
    Less

How to Cite

Mesa, F., Devia-Narváez , D. ., & Ospina-Ospina , R. . (2023). Solution of the traffic flow equation using the finite element method. Revista UIS Ingenierías, 22(2), 65–72. https://doi.org/10.18273/revuin.v22n2-2023006

Copyright (c) 2023 Revista UIS Ingenierías

Creative Commons License

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Abstract

In this document we will study and solve the nonlinear partial differential equation, with initial conditions for vehicle entry that serves to model the dynamics of traffic flow. To find a numerical solution to the dynamics that govern the behavior of traffic flow, the Finite Element Method in a spatial dimension was used. In accordance with the temporal dynamics, simulations were developed to know the flow in terms of time. The numerical solution is interesting for predicting the number of vehicles at the entrance to a high-flow road. Some theorems are enunciated that guarantee the existence of the solution and the uniqueness is given by the boundary conditions.

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