完全耦合一致宏观PDE-ODE系统模拟道路上移动瓶颈的两种算法
Two algorithms for a fully coupled and consistently macroscopic PDE-ODE system modeling a moving bottleneck on a road
摘要：
在本文中，我们提出了两个数值算法来解决耦合的PDE-ODE系统模型的缓慢车辆（瓶颈）与其他汽车一起在道路上移动。由此产生的系统是完全耦合的，因为慢速车辆的动力学取决于汽车的密度，同时，它会导致道路的容量下降，从而限制汽车流量。第一种算法，基于波前跟踪方法，是适合的理论研究和收敛结果。第二种格式基于Goddom格式，用于数值模拟。多个瓶颈的情况下也进行了研究。
英文摘要：
In this paper we propose two numerical algorithms to solve a coupled PDE-ODE system which models a slow vehicle (bottleneck) moving on a road together with other cars. The resulting system is fully coupled because the dynamics of the slow vehicle depends on the density of cars and, at the same time, it causes a capacity drop in the road, thus limiting the car flux. The first algorithm, based on the Wave Front Tracking method, is suitable for theoretical investigations and convergence results. The second one, based on the Godunov scheme, is used for numerical simulations. The case of multiple bottlenecks is also investigated.
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