A Hybrid HWENO Scheme for a Multi-class Traffic Flow Model with Heterogeneous Factors on Highroad

Qi Meng; Jianxian Qiu

doi:10.1007/s42967-024-00470-2

Communications on Applied Mathematics and Computation ›› 2026, Vol. 8 ›› Issue (2) :722 -735. DOI: 10.1007/s42967-024-00470-2

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A Hybrid HWENO Scheme for a Multi-class Traffic Flow Model with Heterogeneous Factors on Highroad

Qi Meng ¹
, Jianxian Qiu ¹^,^a

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Abstract

A hybrid fifth-order finite volume Hermite weighted essentially non-oscillatory (HWENO) scheme is applied for the solution of a multi-class traffic flow model (mcLWR model) with heterogeneous factors on the highroad. Since the hybrid HWENO scheme could avoid oscillations near discontinuities while maintaining efficiency and compactness, it can be a reliable numerical method and tool for the simulation and prediction of rapidly changing the traffic flow. The benchmark examples of Riemann problems and traffic signal control problems are given, and results indicate that the hybrid HWENO numerical scheme can obtain the fifth-order precision, and also has higher resolution and accuracy than the hybrid WENO scheme.

Keywords

Hermite weighted essentially non-oscillatory (HWENO) scheme / Multi-class traffic flow model (mcLWR model) / Non-strictly hyperbolicity / Discontinuous flux / Heterogeneous factors on highway / 35L65 / 65M60

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Qi Meng, Jianxian Qiu. A Hybrid HWENO Scheme for a Multi-class Traffic Flow Model with Heterogeneous Factors on Highroad. Communications on Applied Mathematics and Computation, 2026, 8(2): 722-735 DOI:10.1007/s42967-024-00470-2

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