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An analysis of 1D finite-volume methods for geophysical problems on refined grids

机译：精细网格上地球物理问题的一维有限体积方法分析

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This paper examines high-order unstaggered symmetric and upwind finite-volume discretizations of the advection equation in the presence of an abrupt discontinuity in grid resolution. An approach for characterizing the initial amplitude of a parasitic mode as well as its decay rate away from a grid resolution discontinuity is presented. Using a combination of numerical analysis and empirical studies it is shown that spurious parasitic modes, which are artificially generated by the resolution discontinuity, are mostly undamped by symmetric finite-volume schemes but are quickly removed by upwind and semi-Lagrangian integrated mass (SLIM) schemes. Slope/curvature limiting is insufficient to completely remove these modes, especially at low forcing frequencies where the incident wave can act as a carrier of the parasitic mode. Increasing the order of accuracy of the reconstruction at the grid interface is effective at removing noise from the lowest-frequency incident modes, but insufficient at high frequencies. It is shown that this analysis can be extended to the 1D linear shallow-water equations via Riemann invariants.
机译：本文研究了在网格分辨率突然不连续的情况下对流方程的高阶不交错对称和迎风有限体积离散。提出了一种表征寄生模式的初始振幅及其远离网格分辨率不连续性的衰减率的方法。结合数值分析和经验研究，结果表明，由分辨率不连续性人为产生的寄生寄生模式在很大程度上不受对称有限体积方案的抑制，但很快被逆风和半拉格朗日积分（SLIM）消除计划。斜率/曲率限制不足以完全消除这些模式，尤其是在低强迫频率下，其中入射波可以充当寄生模式的载体。在网格接口处，提高重构精度的顺序可有效消除最低频率入射模式中的噪声，但在高频时则不足。结果表明，该分析可以通过黎曼不变量扩展到一维线性浅水方程。

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