Semi-analytic boundary handling below particle resolution for smoothed particle hydrodynamics

In this paper, we present a novel semi-analytical boundary handling method for spatially adaptive and divergence-free smoothed particle hydrodynamics (SPH) simulations, including two-way coupling. Our method is consistent under varying particle resolutions and allows for the treatment of boundary features below the particle resolution. We achieve this by first introducing an analytic solution to the interaction of SPH particles with planar boundaries, in 2D and 3D, which we extend to arbitrary boundary geometries using signed distance fields (SDF) to construct locally planar boundaries. Using this boundary-integral-based approach, we can directly evaluate boundary contributions, for any quantity, allowing an easy integration into state of the art simulation methods. Overall, our method improves interactions with small boundary features, readily handles spatially adaptive fluids, preserves particle-boundary interactions across varying resolutions, can directly be implemented in existing SPH methods, and, for non-adaptive simulations, provides a reduction in memory consumption as well as an up to 2× speedup relative to current particle-based boundary handling approaches.