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针对交通流LWR模型的数值求解,基于Ismail熵相容理论,推导出相应的熵相容格式;并在空间方向采用CWENO重构,时间方向采用优化三阶Runge-Kutta方法改进该算法,进而得到高精度、高分辨率及数值稳定的熵相容方法。最终将新构造的数值求解格式应用于多个实际交通现象的数值求解当中。数值结果显示:熵相容算法及高分辨率熵相容算法能够避免稀疏-激波现象地产生,在间断区域没有非物理振荡;且高分辨率熵相容算法数值稳定性强,比已有的几种算法分辨率高(激波仅需2~3个过渡点,稀疏波、接触间断与参考值吻合很好),新算法具有TVB(Total Variations Bounded)性,是一种具有实际应用价值的算法。
Aiming at the numerical solution of traffic flow LWR model, based on Ismail entropy compatibility theory, the corresponding entropy compatibility format is deduced. The CWENO reconstruction is used in the spatial direction and the improved third-order Runge-Kutta method is used to improve the algorithm. High precision, high resolution and numerical stability entropy compatible method. Finally, the newly constructed numerical solution is applied to the numerical solution of several real traffic phenomena. The numerical results show that the entropy-compatible algorithm and the high-resolution entropy-compatible algorithm can avoid sparse-shock phenomena and have no non-physical oscillation in the discontinuous region. The high-resolution entropy-compatible algorithm is more stable than the existing The proposed algorithm has the characteristics of Total Variations Bounded (TVB), which is a kind of practical method with high resolution (the shock only needs 2 ~ 3 transition points, the sparse wave, the contact break is in good agreement with the reference value) Algorithm.