连续交通流模型的有限差分近似解法分析

Finite Difference Approximate Solution Analysis of Continuous Traffic Flow Model

连续交通流模型是一个双曲线型偏微分方程式,不易求解,因此一般通过有限差分法近似求解。以均匀到达车流遇停等车队产生向上游回溯冲击波,以及停等车队起动向下游疏解这2种严苛交通案例,研究Lax-F差分法对不同阶连续交通流模型的适用性分析。分析结果表明:Lax-F有限差分法无论是针对1阶准线性连续交通流模型(即LWR模型)还是高阶连续交通流模型,均能获得与解析解相近的近似解,且具有较好的稳定性与收敛性,适用性也良好。

The continuous traffic flow model is a hyperbolic partial differential equation,which is not easy to solve,so it is usually solved by finite difference method. This paper takes 2 severe traffic cases like average traffic flow meet with traffic catchment and generate backflow shock wave,and stopped traffic flow starts moving as examples to study the application of Lax-F difference method to different continuous traffic flow model. Results show： Lax-F infinite differential method is able to obtain similar solution with that by Analytical solution no matter in 1-order quasi-linear continuous traffic flow model（ i. e. LWR model） or high order continuous traffic flow model,and it has good stability,convergence and applicability.