Numerical solutions of a multi-class traffic flow model on an inhomogeneous highway using a high-resolution relaxed scheme

Jian-zhong CHEN; Zhong-ke SHI; Yan-mei HU

doi:10.1631/jzus.C10a0406

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Numerical solutions of a multi-class traffic flow model on an inhomogeneous highway using a high-resolution relaxed scheme

计算机工程 | Updated：2022-12-09

- Numerical solutions of a multi-class traffic flow model on an inhomogeneous highway using a high-resolution relaxed scheme
- Numerical solutions of a multi-class traffic flow model on an inhomogeneous highway using a high-resolution relaxed scheme
- 信息与电子工程前沿（英文） 2012年13卷第1期页码：29-36
- Affiliations：
  
  1.College of Automation, Northwestern Polytechnical University, Xi'an 710072, China
  2.College of Science, Chang'an University, Xi'an 710064, China
- Author bio：
  
  [ "Jian-zhong CHEN, E-mail: jzhchen@nwpu.edu.cn" ]
- Funds：
  
  Project supported by the National Natural Science Foundation of China (No. 11102165) and the Special Fund for Basic Scientific Research of Central Colleges, Chang'an University, China (No. CHD 2011JC039)
- DOI：10.1631/jzus.C10a0406
  中图分类号： TP39;U49
- 收稿：2010-09-16，
  
  修回：2011-12-;5，
  
  纸质出版：2012-01
- Accepted：
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Numerical solutions of a multi-class traffic flow model on an inhomogeneous highway using a high-resolution relaxed scheme[J]. 信息与电子工程前沿（英文）, 2012,13(1):29-36.

Jian-zhong CHEN, Zhong-ke SHI, Yan-mei HU. Numerical solutions of a multi-class traffic flow model on an inhomogeneous highway using a high-resolution relaxed scheme[J]. Frontiers of Information Technology & Electronic Engineering, 2012, 13(1): 29-36.
Numerical solutions of a multi-class traffic flow model on an inhomogeneous highway using a high-resolution relaxed scheme[J]. 信息与电子工程前沿（英文）, 2012,13(1):29-36. DOI： 10.1631/jzus.C10a0406.

Jian-zhong CHEN, Zhong-ke SHI, Yan-mei HU. Numerical solutions of a multi-class traffic flow model on an inhomogeneous highway using a high-resolution relaxed scheme[J]. Frontiers of Information Technology & Electronic Engineering, 2012, 13(1): 29-36. DOI： 10.1631/jzus.C10a0406.

摘要

Abstract

A high-resolution relaxed scheme which requires little information of the eigenstructure is presented for the multiclass Lighthill-Whitham-Richards (LWR) model on an inhomogeneous highway. The scheme needs only an estimate of the upper boundary of the maximum of absolute eigenvalues. It is based on incorporating an improved fifth-order weighted essentially non-oscillatory (WENO) reconstruction with relaxation approximation. The scheme benefits from the simplicity of relaxed schemes in that it requires no exact or approximate Riemann solvers and no projection along characteristic directions. The effectiveness of our method is demonstrated in several numerical examples.

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references

M.K. Banda . . Variants of relaxed schemes and two-dimensional gas dynamics . . J. Comput. Appl. Math. , , 2005 . . 175 ( ( 1 ): ): 41 - - 62 . . DOI: 10.1016/j.jcam.2004.06.008 http://doi.org/10.1016/j.jcam.2004.06.008 . .

M.K. Banda . . Non-oscillatory relaxation schemes for one-dimensional ideal magnetohydrodynamic equations . . Nonl. Anal. Real World Appl. , , 2009 . . 10 ( ( 6 ): ): 3345 - - 3352 . . DOI: 10.1016/j.nonrwa.2008.09.024 http://doi.org/10.1016/j.nonrwa.2008.09.024 . .

M.K. Banda , , , M. Sead . . Higher-order relaxation schemes for hyperbolic systems of conservation laws . . J. Numer. Math. , , 2005 . . 13 ( ( 3 ): ): 171 - - 196 . . DOI: 10.1515/156939505774286102 http://doi.org/10.1515/156939505774286102 . .

M.K. Banda , , , M. Sead . . Relaxation WENO schemes for multidimensional hyperbolic systems of conservation laws . . Numer. Methods Part. Differ. Equat. , , 2007 . . 23 ( ( 5 ): ): 1211 - - 1234 . . DOI: 10.1002/num.20218 http://doi.org/10.1002/num.20218 . .

R. Borges , , , M. Carmona , , , B. Costa , , , W.S. Don . . An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws . . J. Comput. Phys. , , 2008 . . 227 ( ( 6 ): ): 3191 - - 3211 . . DOI: 10.1016/j.jcp.2007.11.038 http://doi.org/10.1016/j.jcp.2007.11.038 . .

R. Brger , , , A. Garca , , , K.H. Karlsen , , , J.D. Towers . . A family of numerical schemes for kinematic flows with discontinuous flux . . J. Eng. Math. , , 2008 . . 60 ( ( 3-4 ): ): 387 - - 425 . . DOI: 10.1007/s10665-007-9148-4 http://doi.org/10.1007/s10665-007-9148-4 . .

J.Z. Chen , , , Z.K. Shi . . Application of a fourth-order relaxation scheme to hyperbolic systems of conservation laws . . Acta Mech. Sin. , , 2006 . . 22 ( ( 1 ): ): 84 - - 92 . . DOI: 10.1007/s10409-005-0079-x http://doi.org/10.1007/s10409-005-0079-x . .

J.Z. Chen , , , Z.K. Shi , , , Y.M. Hu . . A relaxation scheme for a multi-class Lighthill-Whitham-Richards traffic flow model . . J. Zhejiang Univ.-Sci. A , , 2009 . . 10 ( ( 12 ): ): 1835 - - 1844 . . DOI: 10.1631/jzus.A0820829 http://doi.org/10.1631/jzus.A0820829 . .

J.S. Drake , , , J.L. Schofer , , , A.D. May . . A statistical analysis of speed density hypothesis . . Highway Res. Rec. , , 1967 . . 154 53 - - 87 . . . .

S. Gottlieb , , , C.W. Shu , , , E. Tadmor . . Strong stability preserving high order time discretization methods . . SIAM Rev. , , 2001 . . 43 ( ( 1 ): ): 89 - - 112 . . DOI: 10.1137/S003614450036757X http://doi.org/10.1137/S003614450036757X . .

S. Jin , , , Z. Xin . . The relaxation schemes for systems of conservation laws in arbitrary space dimensions . . Commun. Pure Appl. Math. , , 1995 . . 48 ( ( 3 ): ): 235 - - 276 . . DOI: 10.1002/cpa.3160480303 http://doi.org/10.1002/cpa.3160480303 . .

M.J. Lighthill , , , G.B. Whitham . . On kinematic waves (Ⅱ): a theory of traffic flow on long crowed roads . . Proc. R. Soc. Ser. A , , 1955 . . 229 ( ( 1178 ): ): 317 - - 345 . . DOI: 10.1098/rspa.1955.0089 http://doi.org/10.1098/rspa.1955.0089 . .

D. Ngoduy . . Multiclass first-order modelling of traffic networks using discontinuous flow-density relationships . . Transportmetrica , , 2010 . . 6 ( ( 2 ): ): 121 - - 141 . . DOI: 10.1080/18128600902857925 http://doi.org/10.1080/18128600902857925 . .

P.I. Richards . . Shock waves on the highway . . Oper. Res. , , 1956 . . 4 ( ( 1 ): ): 42 - - 51 . . DOI: 10.1287/opre.4.1.42 http://doi.org/10.1287/opre.4.1.42 . .

G.C.K. Wong , , , S.C. Wong . . A multi-class traffic flow model-an extension of LWR model with heterogeneous drivers . . Transp. Res. Part A , , 2002 . . 36 ( ( 9 ): ): 827 - - 841 . . DOI: 10.1016/S0965-8564(01)00042-8 http://doi.org/10.1016/S0965-8564(01)00042-8 . .

M.P. Zhang , , , C.W. Shu , , , G.C.K. Wong , , , S.C. Wong . . A weighted essentially non-oscillatory numerical scheme for a multi-class Lighthill-Whitham-Richards traffic flow model . . J. Comput. Phys. , , 2003 . . 191 ( ( 2 ): ): 639 - - 659 . . DOI: 10.1016/S0021-9991(03)00344-9 http://doi.org/10.1016/S0021-9991(03)00344-9 . .

P. Zhang , , , R.X. Liu , , , S.C. Wong , , , S.Q. Dai . . Hyperbolicity and kinematic waves of a class of multi-population partial differential equations . . Eur. J. Appl. Math. , , 2006a . . 17 ( ( 2 ): ): 171 - - 200 . . DOI: 10.1017/S095679250500642X http://doi.org/10.1017/S095679250500642X . .

P. Zhang , , , S.C. Wong , , , C.W. Shu . . A weighted essentially non-oscillatory numerical scheme for a multi-class traffic flow model on an inhomogeneous highway . . J. Comput. Phys. , , 2006b . . 212 ( ( 2 ): ): 739 - - 756 . . DOI: 10.1016/j.jcp.2005.07.019 http://doi.org/10.1016/j.jcp.2005.07.019 . .

P. Zhang , , , S.C. Wong , , , Z.L. Xu . . A hybrid scheme for solving a multi-class traffic flow model with complex wave breaking . . Comput. Methods Appl. Mech. Eng. , , 2008 . . 197 ( ( 45-48 ): ): 3816 - - 3827 . . DOI: 10.1016/j.cma.2008.03.003 http://doi.org/10.1016/j.cma.2008.03.003 . .

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