Gas-kinetic derivation of Navier-Stokes-like traffic equations.
Gas-kinetic derivation of Navier-Stokes-like traffic equations.
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DOI：
10.1103/physreve.53.2366
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发表时间：
1996-03
期刊：
影响因子：
--
通讯作者：
D. Helbing
中科院分区：
文献类型：
--
作者：
D. Helbing
宏观交通模型最近受到了严厉的批评，仅基于松散的类比，并有一些缺陷。因此，本文展示了如何构建一个逻辑上一致的流体动力学交通模型，从基本法律的车辆的加速度和相互作用。这些考虑导致气体动力学交通方程的Paveri-Fontana。它的固定和空间均匀的解决方案意味着平衡关系的“基本”，方差密度关系，和其他数量的部分难以确定的经验。Paveri-Fontana交通方程允许导出宏观矩方程，从而建立非封闭方程组。这个系统可以封闭的Chapman和Enskog的方法，导致Euler-like交通方程的零阶近似和Navier-Stokes-like交通方程的一阶近似。后者最后根据车辆有限的空间要求进行了修正。结果表明，由此产生的模型是能够承受上述批评。
Macroscopic traffic models have recently been severely criticized to base on lax analogies only and to have a number of deficiencies. Therefore, this paper shows how to construct a logically consistent fluid-dynamic traffic model from basic laws for the acceleration and interaction of vehicles. These considerations lead to the gas-kinetic traffic equation of Paveri-Fontana. Its stationary and spatially homogeneous solution implies equilibrium relations for the `fundamental diagram', the variance-density relation, and other quantities which are partly difficult to determine empirically. Paveri-Fontana's traffic equation allows the derivation of macroscopic moment equations which build a system of non-closed equations. This system can be closed by the well proved method of Chapman and Enskog which leads to Euler-like traffic equations in zeroth-order approximation and to Navier-Stokes-like traffic equations in first-order approximation. The latter are finally corrected for the finite space requirements of vehicles. It is shown that the resulting model is able to withstand the above mentioned criticism.