求解二相LWR交通流模型的低耗散中心迎风格式
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摘要
将求解双曲型守恒律方程的低耗散中心迎风格式和5阶WENO-ZQ格式相结合,推广应用于求解二相LWR交通流模型方程.并在时间方向上推进采用具有强稳定性的4阶Rung-Kutta方法.最后结合Riemann问题及现实生活所遇到的交通流现象进行设计和分析.通过数值算例证明该格式具较强的稳定性和较高的精度,得到了令人满意的结果.
A low dissipation semi-discrete central-upwind scheme for solving the hyperbolic conservation laws equation is extended to Two-phase traffic flow LWR model. The accuracy is improved by employing the high-resolution and high order accuracy fifth order WENO-ZQ reconstruction. Time integration is carried out with strong stability preserving Runge-Kutta method. Numerical results demonstrate that the scheme is more stable and accurate in solving the two-phase traffic flow LWR model. It achieved satisfactory numerical results.
A low dissipation semi-discrete central-upwind scheme for solving the hyperbolic conservation laws equation is extended to Two-phase traffic flow LWR model. The accuracy is improved by employing the high-resolution and high order accuracy fifth order WENO-ZQ reconstruction. Time integration is carried out with strong stability preserving Runge-Kutta method. Numerical results demonstrate that the scheme is more stable and accurate in solving the two-phase traffic flow LWR model. It achieved satisfactory numerical results.
引文
[1] Lighthill M J, Whitham G B. On kinematic wave(II):a theory of traffic flow on long crowed roads[J]. Proceedings of the Royal Society of London, Series A, 1955, 229(1178):317-345.
[2] Richards P I. Shock wave on the highway[J]. Operations Research, 1956, 4(1):42-51.
[3] Wong G C K, Wong S C. A multi class traffic flow model:An extension of LWR model with heterogeneous driver[J]. Transportation Research Part A, 2002, 36(9):827-841.
[4] Zhang P,Liu R X,Dai S Q. Theoretical analysis and numerical simulation on a two-phase traffic flow LWR model[J]. Journal of University of Science and Technology of China. 2005, 35(1):1-11.
[5]胡彦梅,陈建忠,封建湖.双曲守恒律的一种五阶半离散中心迎风格式[J].计算物理,2008, 25(1):29-35.
[6] Kurganov A, Lin C T. On the reduction of numerical dissipation in central-upwind schemes[J].Communications in Computational Physics, 2007, 2(1):141-163.
[7] Balsara S D, Garain S, Shu C W. An efficient class of WENO schemes with adaptive order[J].Journal of Computational Physics, 2016, 326:780-804.
[8] Jang S G, Shu C W. Efficient implementation of weighted ENO schemes[J]. Journal of Computational Physics, 1996, 126(1):202-212.
[9] Jang S G, Wu C C. A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics[J]. Journal of Computational Physics, 1999, 159(2):261-285.
[10]郑素佩,封建湖,曹志杰.求解双曲守恒律方程的5阶CWENO格式[J].昆明理工大学学报(理工版),2005, 30(1):118-120.
[2] Richards P I. Shock wave on the highway[J]. Operations Research, 1956, 4(1):42-51.
[3] Wong G C K, Wong S C. A multi class traffic flow model:An extension of LWR model with heterogeneous driver[J]. Transportation Research Part A, 2002, 36(9):827-841.
[4] Zhang P,Liu R X,Dai S Q. Theoretical analysis and numerical simulation on a two-phase traffic flow LWR model[J]. Journal of University of Science and Technology of China. 2005, 35(1):1-11.
[5]胡彦梅,陈建忠,封建湖.双曲守恒律的一种五阶半离散中心迎风格式[J].计算物理,2008, 25(1):29-35.
[6] Kurganov A, Lin C T. On the reduction of numerical dissipation in central-upwind schemes[J].Communications in Computational Physics, 2007, 2(1):141-163.
[7] Balsara S D, Garain S, Shu C W. An efficient class of WENO schemes with adaptive order[J].Journal of Computational Physics, 2016, 326:780-804.
[8] Jang S G, Shu C W. Efficient implementation of weighted ENO schemes[J]. Journal of Computational Physics, 1996, 126(1):202-212.
[9] Jang S G, Wu C C. A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics[J]. Journal of Computational Physics, 1999, 159(2):261-285.
[10]郑素佩,封建湖,曹志杰.求解双曲守恒律方程的5阶CWENO格式[J].昆明理工大学学报(理工版),2005, 30(1):118-120.