道路交通的流体物理模型与粒子仿真方法

崔曼; 薛惠锋; 陈福振; 卜凡彪

doi:10.7498/aps.66.224501

摘要

针对受多种因素影响的复杂道路交通系统问题，基于颗粒动力学理论，结合传统的Lighthill-Whitham-Richards物理模型，建立道路交通系统的流体物理模型，采用无网格粒子与网格相结合的方法进行数值仿真，并应用于典型道路交通问题的求解.在新模型中，将车辆比拟为硬颗粒，车辆的跟车比拟为颗粒间的碰撞相互作用，已知道路情况对驾驶员操作车辆的影响比拟为流-粒两相系统中的外部流体驱动力作用，不同车道间车辆的影响比拟为颗粒间的黏性作用，从而在颗粒动力学理论的基础上，推导建立了道路交通系统拟流体模型；引入光滑离散颗粒流体动力学（SDPH）对车辆系统模型进行离散，建立SDPH车辆与真实车辆之间的一一对应关系，再结合有限体积方法，对道路交通构建的双流体模型进行求解，建立求解交通流体物理模型的新型仿真方法.最后，采用所建立的模型和方法对车辆汇入以及机非混合对交通系统的影响过程进行了数值仿真，所得结果与实测值符合较好，表明新的模型和方法有效性好、可靠性高，为道路交通问题的解决提供了一条全新的途径.

关键词:

Abstract

The rapid development of social economy speeds up urbanization, but also brings urban traffic congestion and urban traffic problems, such as frequent accidents, energy consumption and environmental pollution. Road traffic, as a part of the most important components in city traffic, is a complex system problem. To solve the difficulties in current city development and people's production and living, and to promote the development of national economy and society greatly, we need to study the road traffic. In order to solve the problem of complex road traffic system influenced by many factors, a physics model of pseudo-fluid of macroscopic road traffic system is established in combination with the traditional Lighthill-Whitham-Richards physics model based on kinetic theory of granular flow. A coupling method of meshless particles with grid is adopted to solve the new traffic model, which is then applied to solving the typical traffic problems. In the new model, vehicles are likened to hard particles. Car-following is likened to collision interactions between particles. Driver driving affected by known road conditions is likened to the driving force exerted by external fluid in two-phase system consisting of fluid and particle, and the influence of vehicles in different lanes is likened to viscous effect between particles. Thus the pseudo-fluid model of road traffic system is deduced and established based on the kinetic theory of granular flow. Then, the traffic multiphase system model is established by adding pedestrians and other non-motorized vehicles to the particles with different attributes. The boundary model of road traffic system based on pipeline theory is established through comparing the boundary model of traffic lights, barricades and forbidden lane changes to wall boundary conditions. Therefore, a complex large traffic model with different initial and boundary conditions considering the complex factors of the system is established. The Smoothed discrete particle hydrodynamics (SDPH) is used to discretize the vehicle system model. A one-to-one correspondence between SDPH vehicles and real vehicles is established through adding the vehicle flow properties characterized by SDPH particles. Then the two-fluid model of road traffic system is solved by combining the finite volume method. Thus, a new simulation approach to solving the macroscopic model of traffic flow is established. Finally, the effects of mixed flow composed of motorized and non-motorized vehicles and vehicles merging on the road traffic are simulated by employing the established model and method. The real-time distribution of the vehicle on the road is obtained, and the variation of the vehicle flow density with time is analyzed. The simulation results are in good agreement with the measured values, which shows that the new model and method are effective and reliable, and they provide a new way of solving the road traffic problem.

Keywords:

作者及机构信息

1.
西北工业大学自动化学院, 西安 710072;

2.
中国航天系统科学与工程研究院, 北京 100048;

3.
火箭军工程大学动力工程系, 西安 710025

通信作者: 陈福振, chen_fu_zhen@163.com

基金项目: 国家自然科学基金（批准号：U1501253，11502132）和陕西省教育厅科研项目（批准号：14JK1132）资助的课题.

Authors and contacts

1.
School of Automation, Northwestern Polyechnical University, Xi'an 710072, China;

2.
China Aerospace Academy of Systems Science and Engineering, Beijing 100048, China;

3.
Dapartment of Power Enginneering, Rocket Engineering University, Xi'an 710025, China

Corresponding author: Chen Fu-Zhen, chen_fu_zhen@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. U1501253, 11502132) and the Research project of the Education Department of Shaanxi Province, China (Grant No. 14JK1132).

参考文献

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[7]	Gan J C, Xiao X C 2003 Acta Phys. Sin. 52 2995 (in Chinese) [甘建超, 肖先赐 2003 52 2995]
[8]	Pipes L A 1900 Transport. Res. 1 21
[9]	Kesting A, Treiber M 2008 Transport. Res. Rec. 2088 148
[10]	Saifuzzaman M, Zheng Z 2014 Transport. Res. C: Emer. 48 379
[11]	Chakroborty P, Kikuchi S 1999 Transport. Res. C: Emer. 7 209
[12]	Wolfram S 1984 Nature 311 419
[13]	Li X, Wu Q, Jiang R 2001 Phys. Rev. E 64 66128
[14]	Pandey G, Rao K R, Mohan D 2015 A Review of Cellular Automata Model for Heterogeneous Traffic Conditions (Berlin: Springer International Publishing) p471
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[17]	Richards P I 1956 Oper. Res. 4 42
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[27]	Prigogine I, Herman R, Schechter R S 2008 IEEE Trans. Syst. Man 2 295
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[37]	Chen F Z, Qiang H F, Gao W R 2015 Comput. Chem. Eng. 77 135
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[39]	Chen F Z, Qiang H F, Gao W R 2014 Acta Phys. Sin. 63 230206 (in Chinese) [陈福振, 强洪夫, 高巍然 2014 63 230206]
[40]	Chen F Z, Qiang H F, Miao G, Gao W R 2015 Acta Phys. Sin. 64 110202 (in Chinese) [陈福振, 强洪夫, 苗刚, 高巍然 2015 64 110202]
[41]	Chen F Z, Qiang H F, Gao W R, Zhou S (in Chinese) [陈福振, 强洪夫, 高巍然, 周算 2015 推进技术 36 175]
[42]	Schiller L, Naumann Z 1935 Zeitschrift des Vereins Deutscher Ingenieure 77 318
[43]	Li W Q, Wang W, Li T Z, Li D M 2002 J. Southeast Univ. 32 252 (in Chinese) [李文权, 王炜, 李铁柱, 李冬梅 2002 东南大学学报 32 252]
[44]	Ouyang J X 2014 Ph. D. Dissertation (Shanghai: Tongji University) (in Chinese) [欧阳吉祥 2014 博士学位论文 (上海: 同济大学)]
[45]	Guan H Z, Chen Y Y, Liu X M, Ren F T (in Chinese) [关宏志, 陈艳艳, 刘小明, 任福田 2001 北京工业大学学报 27 12]
[46]	Liu L H, Guan H Z (in Chinese) [刘兰辉, 关宏志 2000 北京工业大学学报 26 46]
[47]	Jia N, Ma S F (in Chinese) [贾宁, 马寿峰 2011 系统仿真学报 23 390]
[48]	Feng X, Wang X F 2016 J. Highway Transport. Res. Devel. 33 132 (in Chinese) [冯雪, 王喜富 2016 公路交通科技 33 132]

施引文献

[1]	Zhang Y Y, Wu Z, Guo M H 2011 J. Fudan Univ. 6 767 (in Chinese) [张英莹, 吴正, 郭明旻 2011 复旦学报(自然科学版) 6 767]
[2]	Treiber M, Hennecke A, Helbing D 2000 Phys. Rev. E 62 1805
[3]	Chen R, Dong L Y 2005 J. Shanghai Univ. 1 93 (in Chinese) [陈然, 董力耘 2005 上海大学学报 (自然科学版) 1 93]
[4]	Buendia G M, Viswanathan G M, Kenkre V M 2008 Phys. Rev. E 78 56110
[5]	Gao Z Y, Li K P 2005 Chin. Phys. Lett. 22 2711
[6]	Zhang J S, Xiao X C 2000 Acta Phys. Sin. 49 403 (in Chinese) [张家树, 肖先赐 2000 49 403]
[7]	Gan J C, Xiao X C 2003 Acta Phys. Sin. 52 2995 (in Chinese) [甘建超, 肖先赐 2003 52 2995]
[8]	Pipes L A 1900 Transport. Res. 1 21
[9]	Kesting A, Treiber M 2008 Transport. Res. Rec. 2088 148
[10]	Saifuzzaman M, Zheng Z 2014 Transport. Res. C: Emer. 48 379
[11]	Chakroborty P, Kikuchi S 1999 Transport. Res. C: Emer. 7 209
[12]	Wolfram S 1984 Nature 311 419
[13]	Li X, Wu Q, Jiang R 2001 Phys. Rev. E 64 66128
[14]	Pandey G, Rao K R, Mohan D 2015 A Review of Cellular Automata Model for Heterogeneous Traffic Conditions (Berlin: Springer International Publishing) p471
[15]	Jiang R, Wu Q S, Wang B H 2002 Phys. Rev. E 66 36104
[16]	Lighthill M J, Whitham G B 1955 Proc. Royal Soc. 229 317
[17]	Richards P I 1956 Oper. Res. 4 42
[18]	Payne H J 1971 Math. Model Public Syst. 28 51
[19]	Papageorgiou M, Posch B, Schmidt G 1983 Transport.Res. B: Meth. 17 107
[20]	Papageorgiou M 1983 Applications of Automatic Control Concepts to Traffic Flow Modeling and Control (Berlin: Springer-Verlag) p50
[21]	Khne R D 1989 International Conference on Applications of Advanced Technologies in Transportation Engineering San Diego, February 5-8 1989 p287
[22]	Khne R D 1984 The Ninth International Symposium on Transportation and Traffic Theory Delft, Netherlands, July 11-13, 1984 p21
[23]	Michalopoulos P G, Beskos D E, Lin J K 1984 Transport. Res. B: Meth. 18 409
[24]	Helbing D 1998 Phys. Rev. E 55 5498
[25]	Wu Z 1994 Acta Mech. Sin. 26 149 (in Chinese) [吴正 1994 力学学报 26 149]
[26]	Prigogine I, Herman R 1971 Science 173 513
[27]	Prigogine I, Herman R, Schechter R S 2008 IEEE Trans. Syst. Man 2 295
[28]	Herman R, Lam T, Prigogine I 1972 Kinetic Theory of Vehicular Traffic: Comparison with Data (Catonsville: INFORMS) p295
[29]	Bonzani I, Mussone L 2009 Math. Comput. Model. 49 610
[30]	Phillips W F 1979 Transport. Plann. Technol. 5 131
[31]	Ding J, Gidaspow D 1990 AIche J. 36 523
[32]	Jenkins J T, Savage S B 1983 J. Fluid Mech. 130 187
[33]	Lun C K K, Savage S B, Jeffrey D J, Chepurniy N 1984 J. Fluid Mech. 140 223
[34]	Zheng Z, Ahn S, Monsere C M 2010 Accid. Anal. Prev. 42 626
[35]	Li S, Liu W K 2002 Appl. Mech. Rev. 55 1
[36]	Chen F Z, Qiang H F, Zhang H, Gao W R 2017 Int. J. Numer. Meth. Eng. 109 73
[37]	Chen F Z, Qiang H F, Gao W R 2015 Comput. Chem. Eng. 77 135
[38]	Chen F Z, Qiang H F, Gao W R 2014 Acta Phys. Sin. 63 130202 (in Chinese) [陈福振, 强洪夫, 高巍然 2014 63 130202]
[39]	Chen F Z, Qiang H F, Gao W R 2014 Acta Phys. Sin. 63 230206 (in Chinese) [陈福振, 强洪夫, 高巍然 2014 63 230206]
[40]	Chen F Z, Qiang H F, Miao G, Gao W R 2015 Acta Phys. Sin. 64 110202 (in Chinese) [陈福振, 强洪夫, 苗刚, 高巍然 2015 64 110202]
[41]	Chen F Z, Qiang H F, Gao W R, Zhou S (in Chinese) [陈福振, 强洪夫, 高巍然, 周算 2015 推进技术 36 175]
[42]	Schiller L, Naumann Z 1935 Zeitschrift des Vereins Deutscher Ingenieure 77 318
[43]	Li W Q, Wang W, Li T Z, Li D M 2002 J. Southeast Univ. 32 252 (in Chinese) [李文权, 王炜, 李铁柱, 李冬梅 2002 东南大学学报 32 252]
[44]	Ouyang J X 2014 Ph. D. Dissertation (Shanghai: Tongji University) (in Chinese) [欧阳吉祥 2014 博士学位论文 (上海: 同济大学)]
[45]	Guan H Z, Chen Y Y, Liu X M, Ren F T (in Chinese) [关宏志, 陈艳艳, 刘小明, 任福田 2001 北京工业大学学报 27 12]
[46]	Liu L H, Guan H Z (in Chinese) [刘兰辉, 关宏志 2000 北京工业大学学报 26 46]
[47]	Jia N, Ma S F (in Chinese) [贾宁, 马寿峰 2011 系统仿真学报 23 390]
[48]	Feng X, Wang X F 2016 J. Highway Transport. Res. Devel. 33 132 (in Chinese) [冯雪, 王喜富 2016 公路交通科技 33 132]

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