Trans. Planning Journal
|On the Approximation of Finite Difference Methods for Continuum Traffic Flow Models
|Shu-Keng Hsu and Yu-Chiun Chiou
|Because continuum traffic flow models are described by hyperbolic partial differential equations and the exact solutions to the models are difficult to derive analytically, finite difference methods are commonly used to approximate the solutions. In this paper, the fitness of several finite difference methods under different continuum flow models is assessed in two extreme traffic conditions, a backward shock wave formed by a uniform arrival flow encountering a stopped flow and a forward shock wave formed by a discharging flow. The results show that the Lax-F method can obtain good approximations for both the first-order quasi-linear continuum model (i.e., the LWR model) and the high-order continuum flow model with good stability and convergence. This finding is different from previous domestic and foreign studies primarily because past studies examined only traffic cases with uncongested traffic conditions and because of the drawbacks of the Payne model itself.