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A paraboloid fitting technique for calculating curvature from piecewise-linear interface reconstructions on 3D unstructured meshes

机译:一种抛物面拟合技术,用于计算3D非结构化网格上的分段线性界面重建曲率

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摘要

We present a novel method for calculating interface curvature on 3Dunstructured meshes from piecewise-linear interface reconstructions typicallygenerated in the volume of fluid method. Interface curvature is a necessaryquantity to calculate in order to model surface tension driven flow. Curvatureneeds only to be computed in cells containing an interface. The approachrequires a stencil containing only neighbors sharing a node with a target cell,and calculates curvature from a least-squares paraboloid fit to the interfacereconstructions. This involves solving a 6x6 symmetric linear system in eachmixed cell. We present verification tests where we calculate the curvature of asphere, an ellipsoid, and a sinusoid in a 3D domain on regular Cartesianmeshes, distorted hex meshes, and tetrahedral meshes. For both regular andunstructured meshes, we find in all cases the paraboloid fitting method forcurvature to converge between first and second order with grid refinement.
机译:我们提出了一种新的方法,用于在流体法量中的分段 - 线性界面重建从分段 - 线性界面重建计算界面曲率的新方法。界面曲率是计算表面张力驱动流动的必要性。仅在包含接口的单元中计算曲率抑制器。该方法仅包含与目标小区共享节点的邻居的模板,并从最小二乘抛物面拟合拟合界面的曲折。这涉及在每种混合单元中求解6×6对称线性系统。我们呈现验证测试,在普通笛卡尔植物,扭曲的六角网格和四面体网格上,我们计算亚当啤酒,椭球和正弦曲线的曲率。对于常规和谐结构网格,我们发现抛物面拟合方法的所有情况都要粗糙,以汇聚在第一和二阶与网格精制之间。

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