A positioning algorithm for SPH ghost particles in smoothly curved geometries

An algorithm to place ghost particles across the domain boundary in the context of Smoothed Particle Hydrodynamics (SPH) is derived from basic principles, and constructed for several simple, three-dimensional, geometries. The performance of the algorithm is compared against the more commonly used ‘‘mirrored with respect to the local tangent plane" approach and shown to converge to it whenever the distance of the particles to the reflecting boundary is much smaller than a local measure of the surface’s curvature. The algorithm is demonstrated, tested and compared against the usual approach via simulations of a compressible flow around a cylinder, and the numerical cost of implementing it is addressed. We conclude that use of ghost particles to enforce boundary conditions is not only viable in the presence of smoothly curved boundaries, but more robust than the usual method for low-resolution scenarios.This research was sponsored in part by the DGICYT (Dirección General de Investigaciones Científicas y Tecnológicas) of Spain under National Project No. ENE2015-68265. Research was also funded in part by the Erasmus Mundus Program: International Doctoral College in Fusion Science and Engineering FUSION-DC, Spain