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.

中文翻译：

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具有不连续通量的守恒高阶交通流模型的黎曼求解器

将守恒的高阶交通流模型（CHO 模型）扩展到具有不连续通量的情况，称为具有不连续通量的 CHO 模型。基于其齐次子系统的独立性和黎曼不变量的性质，讨论了具有不连续通量的齐次CHO模型的黎曼求解器。此外，我们设计了基于黎曼求解器的一阶Godunov方案来求解扩展模型，并证明了数值解的不变域原理。给出了两个数值例子来说明扩展模型和设计方案的有效性。