Asymptotic traveling wave solutions to anisotropic higher-order traffic flow models with viscosities

Yi-Cheng Meng, Zhi-Yang Lin, Xiao-Yang Li, Dian-Liang Qiao, Ming-Min Guo and Peng Zhang
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Yi-Cheng Meng: Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, P. R. China†School of Finance and Mathematics, Huainan Normal University, Huainan 232038, P. R. China
Zhi-Yang Lin: ��School of Economics and Management, Tongji University, Shanghai 200092, P. R. China
Xiao-Yang Li: ��School of Economics and Management, Tongji University, Shanghai 200092, P. R. China
Dian-Liang Qiao: ��School of Economics and Management, Tongji University, Shanghai 200092, P. R. China
Ming-Min Guo: �Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433, P. R. China
Peng Zhang: Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, P. R. China

International Journal of Modern Physics C (IJMPC), 2022, vol. 33, issue 11, 1-17

Abstract: The boundary layer correction method is applied to study asymptotic traveling wave solutions to anisotropic higher-order traffic flow model with viscous coefficient, which clearly indicates that the truncation error between the original and approximate equations is an equivalent infinitesimal of the coefficient. Therefore, the solution is exact in the case when the coefficient vanishes, which corresponds to a certain nonviscous model following the standard hyperbolic and viscous conservation laws. Numerical simulation is implemented to reproduce a typical traveling wave or wide moving jam consisting of a transitional layer (the downstream front) and a shock (the upstream front) profiles, of which the parameters converge not only for refined meshes but for refined viscous coefficient as well. These are highly in agreement with the analytical results.

Keywords: Hyperbolic and viscous conservation laws; boundary layer correction method; transitional layer; shock wave; a wide moving jam (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0129183122501522

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