## Abstract

An extension of the Colombo phase transition model is proposed. The congestion phase is described by a two-dimensional zone defined around a standard fundamental diagram. General criteria for building such a set-valued fundamental diagram are enumerated and instantiated on several standard fluxes with different concavity properties. The solution to the Riemann problem in the presence of phase transitions is obtained through the design of a Riemann solver, which enables the construction of the solution of the Cauchy problem using wavefront tracking. The free-flow phase is described using a Newell-Daganzo fundamental diagram, which allows for a more tractable definition of phase transition compared to the original Colombo phase transition model. The accuracy of the numerical solution obtained by a modified Godunov scheme is assessed on benchmark scenarios for the different flux functions constructed.

Original language | English (US) |
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Pages (from-to) | 107-127 |

Number of pages | 21 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 71 |

Issue number | 1 |

DOIs | |

State | Published - 2011 |

## Keywords

- Hyperbolic systems of conservation laws
- Macroscopic highway traffic flow model
- Numerical scheme
- Partial differential equations
- Phase transition
- Riemann solver

## ASJC Scopus subject areas

- Applied Mathematics