No abstract

This work presents a method of exactly and efficiently evaluating integrals of compactly supported (and otherwise) polynomial radial kernels near piecewise-planar boundaries. The technique is motivated by and has an immediate application in the smoothed-particle hydrodynamics method employing the semi-analytical boundary formulation. The current implementation is exact and fully general, avoiding any need for symbolic or numerical integration which previous implementations rely on. A detailed derivation and three compact implementations are provided and the latter can be easily modified to fit new and existing simulation codes. Applications and good performance are demonstrated on a number of test problems, where the semi-analytical boundary method can simulate complex boundaries using roughly half the boundary particles required in a ghost particle boundary method.

A method for modeling mobile spherical solids in Smoothed Particle Hydrodynamics simulations utilizing the semi-analytical boundary formulation is given. The technique relies on evaluating individual contributions from ideally spherical bodies to the normalization factor and its gradient. A derivation is provided in both two and three dimensions (3D) and a close-form solution is given for an arbitrary polynomial kernel function in 3D. The method is validated and implemented in an Smoothed-Particle Hydrodynamics-Discrete Element Method code to evaluate the solid fraction and results are compared to the previous standard.