Semi‐analytical smoothed‐particle hydrodynamics correction factors for polynomial kernels and piecewise‐planar boundaries

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.