Article ID Journal Published Year Pages File Type
524803 Transportation Research Part C: Emerging Technologies 2014 32 Pages PDF
Abstract

•A common numerical framework for second-order traffic flow models is presented.•The ow models are written in conservation or balance law form.•The relaxation approximation transforms the nonlinear systems to semi-linear ones.•High-resolution finite volume discretizations (in space and time) are utilized.

A novel numerical approach for the approximation of several, widely applied, macroscopic traffic flow models is presented. A relaxation-type approximation of second-order non-equilibrium models, written in conservation or balance law form, is considered. Using the relaxation approximation, the nonlinear equations are transformed to a semi-linear diagonilizable problem with linear characteristic variables and stiff source terms. To discretize the resulting relaxation system, low- and high-resolution reconstructions in space and implicit–explicit Runge–Kutta time integration schemes are considered. The family of spatial discretizations includes a second-order MUSCL scheme and a fifth-order WENO scheme, and a detailed formulation of the scheme is presented. Emphasis is given on the WENO scheme and its performance for solving the different traffic models. To demonstrate the effectiveness of the proposed approach, extensive numerical tests are performed for the different models. The computations reported here demonstrate the simplicity and versatility of relaxation schemes as solvers for macroscopic traffic flow models.

Related Topics
Physical Sciences and Engineering Computer Science Computer Science Applications
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