Riemann solvers of a conserved high-order traffic flow model with discontinuous fluxes

•A conserved high-order traffic flow model (CHO model) is extended to the case with discontinuous fluxes.•The Riemann solvers and wave patterns to the homogeneous CHO model with discontinuous fluxes are discussed.•The numerical algorithm used to solve the CHO model with discontinuous fluxes is designed.•The numerical result shows that the extended model can reproduce stop-and-go waves. A conserved high-order traffic flow model (CHO model) is extended to the case with discontinuous fluxes which is called the CHO model with discontinuous fluxes. Based on the independence of its homogeneous subsystem and the property of Riemann invariants, Riemann solvers to the homogeneous CHO model with discontinuous fluxes are discussed. Moreover, we design the first-order Godunov scheme based on the Riemann solvers to solve the extended model, and prove the invariant region principle of numerical solutions. Two numerical examples are given to illustrate the effectiveness of the extended model and the designed scheme.