SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1119-1144, June 2024.
Abstract. This paper considers numerical discretization of a nonlocal conservation law modeling vehicular traffic flows involving nonlocal intervehicle interactions. The nonlocal model involves an integral over the range measured by a horizon parameter and it recovers the local Lighthill–Richards–Whitham model as the nonlocal horizon parameter goes to zero. Good numerical schemes for simulating these parameterized nonlocal traffic flow models should be robust with respect to the change of the model parameters but this has not been systematically investigated in the literature. We fill this gap through a careful study of a class of finite volume numerical schemes with suitable discretizations of the nonlocal integral, which include several schemes proposed in the literature and their variants. Our main contributions are to demonstrate the asymptotically compatibility of the schemes, which includes both the uniform convergence of the numerical solutions to the unique solution of nonlocal continuum model for a given positive horizon parameter and the convergence to the unique entropy solution of the local model as the mesh size and the nonlocal horizon parameter go to zero simultaneously. It is shown that with the asymptotically compatibility, the schemes can provide robust numerical computation under the changes of the nonlocal horizon parameter.

中文翻译：

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非局部交通流模型的一类数值格式的渐近相容性

《SIAM 数值分析杂志》，第 62 卷，第 3 期，第 1119-1144 页，2024 年 6 月
。摘要。本文考虑对涉及非局部车辆间相互作用的车辆交通流进行建模的非局部守恒定律的数值离散。非局部模型涉及由地平线参数测量的范围内的积分，并且当非局部地平线参数变为零时，它恢复局部 Lighthill-Richards-Whitham 模型。用于模拟这些参数化非局部交通流模型的良好数值方案应该对于模型参数的变化具有鲁棒性，但文献中尚未对此进行系统研究。我们通过仔细研究一类具有适当的非局部积分离散化的有限体积数值格式来填补这一空白，其中包括文献中提出的几种格式及其变体。我们的主要贡献是证明了这些方案的渐近兼容性，其中包括给定正层位参数的非局部连续统模型的唯一解的数值解的一致收敛性以及局部模型的唯一熵解的收敛性：网格尺寸和非局部水平参数同时变为零。结果表明，该方案具有渐进相容性，能够在非局部层位参数变化的情况下提供鲁棒的数值计算。