一种具有最优局部相干平流格式的梯度增强水平集方法
A gradient-augmented level set method with an optimally local, coherent advection scheme
AI总结：
提出一种梯度增强水平集方法，通过完全耦合演化函数值和梯度，利用导数信息保持相干性，实现最优局部模板和亚网格结构追踪。
摘要：
水平集方法隐式表示曲面，并通过在欧拉网格上数值定义的水平集函数的演化来平流曲面。本文提出一种方法，通过梯度信息增强水平集函数值，并以完全耦合的方式演化两者。这保持了函数值与导数之间的相干性，同时利用了导数携带的额外信息。该方法的质量与WENO格式相当，但具有最优局部模板（仅使用单个相邻网格单元的信息进行时间更新）。此外，可以定位和追踪小于网格尺寸的结构，并且可以利用额外的导数信息获得简单而精确的曲率近似。我们分析了新格式的精度和稳定性，并进行了基准测试。
英文摘要：
The level set approach represents surfaces implicitly, and advects them by evolving a level set function, which is numerically defined on an Eulerian grid. Here we present an approach that augments the level set function values by gradient information, and evolves both quantities in a fully coupled fashion. This maintains the coherence between function values and derivatives, while exploiting the extra information carried by the derivatives. The method is of comparable quality to WENO schemes, but with optimally local stencils (performing updates in time by using information from only a single adjacent grid cell). In addition, structures smaller than the grid size can be located and tracked, and the extra derivative information can be employed to obtain simple and accurate approximations to the curvature. We analyze the accuracy and the stability of the new scheme, and perform benchmark tests.
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