无压水动力交通流模型的活塞问题

Zhengqi Wang, Lihui Guo, Zhijian Wei
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引用次数: 0

摘要

流体力学模型可用于描述交通运输中的交通问题。当第一辆车的速度小于后面车辆的速度时,就会导致交通堵塞。当第一辆车的速度快于后面车辆的速度时,就会导致交通疏散。如果我们将第一辆车视为活塞,那么活塞的速度将导致交通堵塞和交通疏散。本文研究了流体力学模型的活塞问题。冲击波、稀释波、三角冲击波和真空的形成和传播可分别描述交通堵塞、交通疏散、严重交通堵塞和交通量为零时的交通疏散现象。因此,针对不同的交通现象,我们证明了冲击波解、稀释波解、三角冲击波解和真空解的存在。此外,我们还进行了一些有代表性的数值模拟。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Piston problem for the pressureless hydrodynamic traffic flow model
The hydrodynamic model can be used to describe traffic problems in transport. When the speed of the first car is less than the speed behind it, it leads to traffic jams. When the first car's speed is faster than the cars behind it, it leads to traffic evacuation. If we consider the first car to be a piston, then the speed of the piston will cause traffic jams and traffic evacuation. In this paper, we study the piston problem for the hydrodynamic model. The formation and propagation of shock wave, rarefaction wave, delta-shock wave, and vacuum can describe the phenomena of traffic jams, traffic evacuation, severe traffic jams, and traffic evacuation with traffic volume of zero, respectively. Therefore, for different traffic phenomena, we prove the existence of shock solution, rarefaction solution, delta shock solution, and vacuum solution. In addition, we perform some representative numerical simulations.
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