A lattice hydrodynamical model considering turning capability
Tian Huan-Huan(田欢欢)a)b) and Xue Yu(薛郁) a)c)†
a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; b College of Physics Science and Engineering, Yulin Normal University, Yulin 537000, China; c Institute of Physics Science and Engineering, Guangxi University, Nanning 530004, China
Abstract A new two-dimensional lattice hydrodynamic model considering the turning capability of cars is proposed. Based on this model, the stability condition for this new model is obtained by using linear stability analysis. Near the critical point, the modified KdV equation is deduced by using the nonlinear theory. The results of numerical simulation indicate that the critical point ac increases with the increase of the fraction p of northbound cars which continue to move along the positive y direction for c=0.3, but decreases with the increase of p for c=0.7. The results also indicate that the cars moving along only one direction (eastbound or northbound) are most stable.
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10865001, 11047003, 11172164, and 11162019) and the Youth Foundation of the Yulin Normal University of China (Grant No. 2011YJQN01).
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