High-resolution numerical approximation of traffic flow problems with variable lanes and free-flow velocities

Area of Science:

• Traffic flow modeling
• Applied mathematics
• Computational fluid dynamics

Background:

• Macroscopic traffic flow models are essential for understanding and managing highway dynamics.
• Existing models often struggle with spatially varying conditions like variable lanes and free-flow velocities.
• Accurate simulation of traffic phenomena, such as bottlenecks, requires robust numerical methods.

Purpose of the Study:

• To develop advanced macroscopic traffic flow models for highways with spatially varying flux functions.
• To create a precise Riemann solver for handling complex interface conditions.
• To formulate efficient Godunov-type numerical schemes for solving these models.

Main Methods:

• Development of a novel Riemann solver to determine exact flux values at interfaces.
• Formulation of Godunov-type numerical schemes based on the developed Riemann solver.
• Application of these schemes to simulate traffic flow dynamics.

Main Results:

• The proposed Riemann solver accurately captures flux variations in heterogeneous traffic environments.
• Godunov-type schemes demonstrate high efficiency in solving the developed traffic flow models.
• Numerical simulations successfully illustrate traffic behavior around capacity-drop bottlenecks.

Conclusions:

• The developed models and numerical schemes provide an effective tool for analyzing traffic flow on highways with variable characteristics.
• The methodology offers improved accuracy and efficiency in simulating complex traffic phenomena like bottlenecks.
• This work contributes to better traffic management and infrastructure planning through advanced modeling techniques.