双车动力学模型的数值模拟改进研究

摘要

选取双车动力学模型描述交通流，用一阶迎风格式和MHM格式寻求了相应的数值解，然后用改进的高阶 MHCM 差分格式得出相应的新的数值解，最后对不同的数值解进行分析比较。数值模拟结果表明，高阶修正MHCM格式耗散小、精度高，而且能更有效的描述交通流的冲击波和疏散波，效果较好。%This paper picks out the two-car dynamical model to describe the traffic flow. Firstly, using the first order upwind scheme and the MHM scheme quests the relevant numerial solution. Then, using the modified high order MHCM scheme obtains the new numerical solution. Finally, the different numerical solutions are analyzed and compared one by one. The simulated result of numerical value indicates that the modified MHCM scheme is better than the old scheme for its small dissipation, high precision and more effective to describe the shock wave and evacuation wave of traffic flow.