迎风嵌入式边界SBP算子：用于笛卡尔网格任意形状域的新高阶数值格式
Upwind embedded boundary SBP operators: New high order numerical schemes for arbitrarily shaped domains with Cartesian grids
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中文总结 AI 辅助
研究在笛卡尔网格任意形状域中提高数值格式精度问题，基于嵌入式边界SBP框架推导新算子，通过推广到迎风格式改善频谱特性，经曲线标量波动方程测试，证明新算子的稳健性和准确性。
中文摘要 AI 辅助
嵌入式边界分部求和（SBP）方法定义了基于有限差分的导数算子，其特点是边界无需与网格单元重合，可将边界嵌入规则笛卡尔网格。通过引入匹配边界封闭精度的插值/外推算子实现。该方法已用于在规则笛卡尔网格中嵌入球形边界的域上进行黑洞切除模拟。本文利用此框架推导新算子，提高内部和边界封闭精度并最小化边界误差，通过推广到迎风格式改善网格频谱特性，在含切除球的三维多块网格上用曲线标量波动方程测试了新算子的稳健性和准确性。
英文摘要
Embedded boundary summation by parts (SBP) methods define finite differencing based derivative operators with the added feature that the boundary need not coincide with a grid cell, allowing a boundary to be embedded on a regular Cartesian grid. This is achieved by the introduction of interpolation/extrapolation operators that match the accuracy of the boundary closure. These methods have been used to perform black hole excision simulations on a domain with a spherical boundary embedded in a regular Cartesian grid, demonstrating their usefulness for nonlinear problems. In this work, new operators are derived using this embedded boundary framework to increase the order of accuracy of the interior and boundary closure while minimizing the boundary error. Additionally, these novel operators improve the spectral properties on the grid by generalizing to an upwind scheme that has better dispersion relation preserving properties compared to traditional SBP schemes for wave equations. These operators are tested with the curvilinear scalar wave equation on a 3D multiblock grid with an excision sphere embedded in the center block to demonstrate the robustness and accuracy of these novel embedded operators.
