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Volume 1, Issue 3
LWDG Method for a Multi-Class Traffic Flow Model on an Inhomogeneous Highway

Tiantian Sun & Jianxian Qiu

Adv. Appl. Math. Mech., 1 (2009), pp. 438-450.

Published online: 2009-01

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  • Abstract

In this paper, we apply the discontinuous Galerkin method with Lax-Wendroff type time discretizations (LWDG) using the weighted essentially non-oscillatory (WENO) limiter to solve a multi-class traffic flow model for an inhomogeneous highway, which is a kind of hyperbolic conservation law with spatially varying fluxes. The numerical scheme is based on a modified equivalent system which is written as a "standard" hyperbolic conservation form. Numerical experiments for both the Riemann problem and the traffic signal control problem are presented to show the effectiveness of these methods.

  • Keywords

Multi-class traffic flow, inhomogeneous highway spatially varying flux, non-strictly hyperbolic conservation laws, LWDG method, WENO limiter.

  • AMS Subject Headings

35L65, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-1-438, author = {Sun , Tiantian and Qiu , Jianxian}, title = {LWDG Method for a Multi-Class Traffic Flow Model on an Inhomogeneous Highway}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2009}, volume = {1}, number = {3}, pages = {438--450}, abstract = {

In this paper, we apply the discontinuous Galerkin method with Lax-Wendroff type time discretizations (LWDG) using the weighted essentially non-oscillatory (WENO) limiter to solve a multi-class traffic flow model for an inhomogeneous highway, which is a kind of hyperbolic conservation law with spatially varying fluxes. The numerical scheme is based on a modified equivalent system which is written as a "standard" hyperbolic conservation form. Numerical experiments for both the Riemann problem and the traffic signal control problem are presented to show the effectiveness of these methods.

}, issn = {2075-1354}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aamm/8380.html} }
TY - JOUR T1 - LWDG Method for a Multi-Class Traffic Flow Model on an Inhomogeneous Highway AU - Sun , Tiantian AU - Qiu , Jianxian JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 438 EP - 450 PY - 2009 DA - 2009/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aamm/8380.html KW - Multi-class traffic flow, inhomogeneous highway KW - spatially varying flux, non-strictly hyperbolic conservation laws, LWDG method, WENO limiter. AB -

In this paper, we apply the discontinuous Galerkin method with Lax-Wendroff type time discretizations (LWDG) using the weighted essentially non-oscillatory (WENO) limiter to solve a multi-class traffic flow model for an inhomogeneous highway, which is a kind of hyperbolic conservation law with spatially varying fluxes. The numerical scheme is based on a modified equivalent system which is written as a "standard" hyperbolic conservation form. Numerical experiments for both the Riemann problem and the traffic signal control problem are presented to show the effectiveness of these methods.

Sun , Tiantian and Qiu , Jianxian. (2009). LWDG Method for a Multi-Class Traffic Flow Model on an Inhomogeneous Highway. Advances in Applied Mathematics and Mechanics. 1 (3). 438-450. doi:
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