High Resolution Schemes for the Numerical Solutions of Macroscopic Continuum Traffic Flow Models

• Main Authors: Feng-Jang Hwang, 黃鋒樟
• Other Authors: Hsun-Jung Cho
• Format: Others
• Language: en_US
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/44888381169878729796

碩士 === 國立交通大學 === 運輸科技與管理學系 === 90 === Numerical simulation is significant to solve macroscopic continuum traffic flow models, which describe various traffic phenomena and play an important role in the development of Intelligent Transport Systems (ITS). Continuum traffic flow models are often analyzed with systems of hyperbolic partial differential equations (PDEs) attended by suitable initial and boundary conditions. Due to difficulty in solving hyperbolic PDEs, numerous numerical methods have been presented to afford a considerable approach attaining the reasonable solution. The first order accurate method yields a numerical diffusion, which causes smoothing of shock fronts, and is inaccurate. However, higher order methods produce unrealistic oscillations close to steep gradients. Such oscillations, which are called the Gibbs phenomena in spectral methods, don’t decay in magnitude when refining the mesh. The objective of the study was to simulate continuum traffic flow models with high resolution methods that improve the numerical precision and eliminate such spurious oscillations near discontinuities. High order Weighted Essentially Non-Oscillatory (WENO) finite difference and finite volume schemes were applied to solve the simple and high order continuum traffic flow models that involve the discontinuous initial conditions and thus are Riemann problems. The numerical solutions of WENO schemes were compared with results produced by Total Variation Diminishing (TVD) type scheme and other numerical methods previously used to solve traffic flow models. Test problems of the simple continuum model, including shock, rarefaction wave, traffic signal, and square wave cases, were shown to illustrate the dominant accuracy of WENO schemes. WENO schemes also exhibited the capability of presenting appropriate results in Riemann problems of high order continuum models with numerical examples, including shock and rarefaction wave problems, for Payne-Whitham (PW) and Jiang’s improved models. The results indicate that WENO schemes can afford to be utilized in the simulation of complex traffic phenomena, such as shock, rarefaction waves, stop-and-go waves, and local cluster effects. In the future, with the implementation of parallel processing the WENO algorithm, parallel high resolution numerical scheme would be a reliable, fast, and robust method for traffic flow simulation.