Exact calculation of the overlap volume of spheres and mesh elements
Exact calculation of the overlap volume of spheres and mesh elements
复制标题
球体与网格单元重叠体积的精确计算
DOI：
10.1016/j.jcp.2016.02.003
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
T. Pöschel
中科院分区：
文献类型：
--
作者：
Severin Strobl;A. Formella;T. Pöschel
本文介绍了一种精确计算球体与四面体、楔形体或六面体的重叠体积的算法。该方法可用于确定一个系统的球形，不重叠的颗粒包含在一个复杂的网格，一个问题的数值解的许多流体-固体相互作用问题的显着相关的精确的局部固体分数。虽然具有挑战性，由于有限的机器精度，一个数值稳健的版本的计算保持高计算效率的设计。该方法的数值精度和计算成本进行评估。结果表明，精确的计算是唯一的机器精度的限制，并可以适用于广泛的尺寸比，与以前公布的方法相反。消除这一约束，使耦合CFD-DEM模拟的系统边界附近的网格具有更高的分辨率的使用。通过将该方法应用于高度变形的网格单元，进一步说明了数值鲁棒性。参考实现的完整源代码在开源许可证下提供。
An algorithm for the exact calculation of the overlap volume of a sphere and a tetrahedron, wedge, or hexahedron is described. The method can be used to determine the exact local solid fractions for a system of spherical, non-overlapping particles contained in a complex mesh, a question of significant relevance for the numerical solution of many fluid-solid interaction problems. While challenging due to the limited machine precision, a numerically robust version of the calculation maintaining high computational efficiency is devised. The method is evaluated with respect to the numerical precision and computational cost. It is shown that the exact calculation is only limited by the machine precision and can be applied to a wide range of size ratios, contrary to previously published methods. Eliminating this constraint enables the usage of meshes with higher resolution near the system boundaries for coupled CFD–DEM simulations. The numerical robustness is further illustrated by applying the method to highly deformed mesh elements. The full source code of the reference implementation is made available under an open-source license.