AI 中文总结
为里帕模型引入五阶平衡良好的路径守恒 A-WENO 格式（PCCU-5），借助通量全局化技术，利用平衡变量的 WENO 插值及局部特征平衡变量的 WENO 插值，经实验验证该格式高分辨率且优于二阶格式，凸显局部特征投影对减少间断处数值振荡的重要性。
AI 中文摘要
在这项工作中，我们为里帕模型引入了一种具有中心迎风数值通量的五阶平衡良好（WB）路径守恒 A-WENO 格式（PCCU-5）。该格式能够精确保持多种稳态，包括静水、动水、等压和恒定水位状态。借助通量全局化技术实现此目标：将源项纳入通量，形成准守恒系统，使用路径守恒积分计算中心迎风数值通量。所提出的 A-WENO 格式利用平衡变量而非守恒变量的 WENO 插值来确保 WB 属性。此外，对局部特征平衡变量进行 WENO 插值以减轻间断附近的数值振荡。进行了一系列数值实验，结果表明所提出的五阶 WB PCCU-5 格式具有高分辨率，明显优于其二阶对应格式。数值结果还证明了局部特征投影对于显著减少（消除）间断附近数值振荡的重要性。
英文摘要
In this work, we introduce a fifth-order well-balanced (WB) path-conservative A-WENO scheme with the central-upwind numerical fluxes (PCCU-5) for the Ripa model. The proposed scheme is capable of exactly preserving a variety of steady states, including still-water, moving-water, isobaric, and constant water height ones. This goal is achieved with the help of a flux globalization technique: The source terms are incorporated into the fluxes, resulting in a quasi-conservative system, for which central-upwind numerical fluxes are computed using the path-conservative integration. The proposed A-WENO scheme utilizes a WENO interpolation of the equilibrium variables rather than the conservative ones to ensure the WB property. In addition, we perform the WENO interpolation of the local characteristic equilibrium variables to mitigate numerical oscillations near discontinuities. We perform a series of numerical experiments, which demonstrate that the proposed fifth-order WB PCCU-5 scheme achieves high resolution and clearly outperforms its second-order counterpart. Our numerical results also demonstrate the importance of the local characteristic projection for significantly reducing (eliminating) numerical oscillations near discontinuities.
