更新幅度状态重分布 (UM-SRD): 用于切割网格的加权SRD的关闭扩展
Update-Magnitude State Redistribution (UM-SRD): A Shut-off Extension of Weighted SRD for Cut-Cell Methods
AI总结：
针对切割网格中加权状态重分布(SRD)无法保持稳态和引入额外耗散的问题，提出基于有限体积更新幅度的UM-SRD方法，通过平滑局部指示器混合SRD与恒等算子，实现守恒性、稳态保持和高阶精度。
摘要：
Berger & Giuliani (2024) 开发了一种可证明稳定的加权状态重分布 (SRD) 算法用于切割网格。他们方法的一个关键限制是，尽管通量重分布在更新较小时自然消失，但 SRD 即使在通量平衡为零时也持续应用重分布，阻止了精确稳态保持，并可能在光滑区域引入不必要的耗散。本文引入了更新幅度状态重分布 (UM-SRD)，它通过一个光滑的、局部定义的有限体积更新幅度标量指示器，将 SRD 算子与恒等算子混合。UM-SRD 保持守恒性，并且当有限体积更新在小区邻域内恰好为零时，精确退化为基本格式。对于具有单个小切割单元的一维模型问题，我们证明了 UM-SRD 在与基本迎风格式相同的 CFL 条件下满足总变差减小性质，展示了使用非归一化指示器时，光滑区域中的局部截断误差修正是高阶的，并且归一化实现保持一阶精度。数值实验在光滑的一维和二维平流测试中证明了收敛到一阶，确认了关闭行为，验证了无振荡性质，提供了数值证据表明 UM-SRD 在基本格式发散的小切割单元附近稳定了基本格式，并确认了精确稳态保持。该算法重用现有的加权 SRD 基础设施，仅添加一个局部混合机制，使其适用于切割网格有限体积代码。
英文摘要：
Berger & Giuliani (2024) developed a provably stable weighted state redistribution (SRD) algorithm for cut-cell meshes. A key limitation of their method is that, although flux redistribution naturally vanishes when updates are small, SRD continuously applies redistribution even when the flux balance is zero, preventing exact steady-state preservation and potentially introducing unnecessary dissipation in smooth regions. This work introduces Update-Magnitude State Redistribution (UM-SRD), which blends the SRD operator with the identity operator via a smooth, locally-defined scalar indicator of the finite-volume update magnitude. UM-SRD preserves conservation and reduces exactly to the base scheme when the finite-volume update is exactly zero in a small-cell neighborhood. For a one-dimensional model problem with a single small cut cell, we prove UM-SRD is total variation diminishing under the same CFL condition as the base upwind scheme, show the local truncation error modification is higher-order in smooth regions with the unnormalized indicator, and show that the normalized implementation preserves first-order accuracy. Numerical experiments demonstrate convergence toward first order on smooth 1D and 2D advection tests, confirm shut-off behaviour, verify non-oscillatory properties, provide numerical evidence that UM-SRD stabilizes the base scheme near a small cut cell where the base scheme diverges, and confirm exact steady-state preservation. The algorithm reuses existing weighted SRD infrastructure, adding only a local blending mechanism, making it practical for cut-cell finite-volume codes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
