Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 311, Issue -, Pages 158-172Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2016.02.003
Keywords
Overlap volume; Local solid fraction; Numerical robustness; Sphere-mesh overlap
Funding
- Deutsche Forschungsgemeinschaft (DFG) through Cluster of Excellence Engineering of Advanced Materials
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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. (C) 2016 Elsevier Inc. Al lrights reserved.
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