Exact calculation of the overlap volume of spheres and mesh elements

Strobl S, Formella A, Pöschel T (2016)

Publication Language: English

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2016


Book Volume: 311

Pages Range: 158-172

DOI: 10.1016/j.jcp.2016.02.003


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.

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Strobl, S., Formella, A., & Pöschel, T. (2016). Exact calculation of the overlap volume of spheres and mesh elements. Journal of Computational Physics, 311, 158-172. https://dx.doi.org/10.1016/j.jcp.2016.02.003


Strobl, Severin, Arno Formella, and Thorsten Pöschel. "Exact calculation of the overlap volume of spheres and mesh elements." Journal of Computational Physics 311 (2016): 158-172.

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