Korteweg–de Vries方程
机械
物理
流量(数学)
理论(学习稳定性)
流量(计算机网络)
非线性系统
转化(遗传学)
经典力学
计算机安全
计算机科学
生物化学
量子力学
基因
机器学习
化学
作者
Peng Zhang,Yu Xue,Yi‐Cai Zhang,Xue Wang,Bing-Lin Cen
标识
DOI:10.1142/s0217984920502176
摘要
In this paper, we deduced a macroscopic traffic model on the uphill and downhill slopes by employing the transformation relation from microscopic variables to macroscopic ones based on a microscopic car-following model considering the velocity difference between adjacent vehicles. The angle [Formula: see text] of the uphill and downhill and the gravitational force have a great impact upon the stability of traffic flow. The linear stability analysis for macroscopic traffic model yielded the stability condition. The Korteweg–de Vries (KdV) equation is derived by nonlinear analysis and the corresponding solution to the density wave near the neutral stability line is obtained. By using the upwind finite difference scheme for simulation, the spatiotemporal evolution patterns of traffic flow on the uphill and downhill are attained. The unstable region is shrunken with slope of the gradient increasing and backward-traveling density waves gradually decrease and even disappear on uphill. Conversely, the unstable region on downhill is extended and density waves propagate quickly backward to the whole road with slope of the gradient increasing.
科研通智能强力驱动
Strongly Powered by AbleSci AI