This paper evaluates and compares the accuracy and robustness of curvature estimation methods for three-dimensional interfaces represented implicitly by discrete volume fractions on a Cartesian mesh. The height function (HF) method is compared to three paraboloid fitting methods: fitting to the piecewise linear interface reconstruction centroids (PC), fitting to the piecewise linear interface reconstruction volumetrically (PV), and volumetrically fitting (VF) the paraboloid directly to the volume fraction field. A shape-independent test of the curvature estimation is introduced through the use of randomly oriented and shaped paraboloids as reference interfaces. The coupling of the curvature estimation, interface transport, and Navier–Stokes surface tension force is evaluated through the measurement of spurious velocities in simulations of stationary and translating droplets. These studies find that while the curvature error from the VF method converges with second-order accuracy as with the HF method for static interfaces represented by exact volume fractions, the PV method best balances low curvature errors with low computational cost when errors are introduced in the volume fraction field either artificially or through the interface advection and reconstruction steps.

中文翻译：

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体积分数曲率估计方法的比较

本文评估并比较了笛卡尔网格上离散体积分数隐式表示的三维界面的曲率估计方法的准确性和鲁棒性。将高度函数 (HF) 方法与三种抛物面拟合方法进行比较：拟合分段线性界面重建质心 (PC)、体积拟合分段线性界面重建 (PV) 以及将抛物面直接体积拟合 (VF)体积分数字段。通过使用随机定向和形状的抛物面作为参考接口，引入了曲率估计的与形状无关的测试。通过测量静止和平移液滴模拟中的杂散速度来评估曲率估计、界面传输和纳维-斯托克斯表面张力的耦合。这些研究发现，虽然 VF 方法的曲率误差与 HF 方法一样以二阶精度收敛，用于由精确体积分数表示的静态界面，但当在人工或通过界面平流和重建步骤生成体积分数场。