Volume mapping of large spherical particles to a Cartesian grid with smaller grid elements is typically required in application of simple immersed boundary conditions in coupled engineering simulations. However, there exists no unique analytical solution to computation of the volume of intersection between spheres and cubes. The purpose of this paper is to determine a suitable solution to this problem depending on the required level of accuracy.
In this work, existing numerical techniques for computing intersection volume are reviewed and compared in terms of accuracy and performance. In addition to this, a more efficient linear relationship is proposed and included in this comparison.
The authors find in this work that a simple linear relationship is both acceptably accurate and more computationally efficient than the contemporary techniques.
This simple linear approach may be applied to accurately compute solutions to fluid-particle systems with very large numbers of particles.
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