Robust Simulation of Sparsely Sampled Thin Features in SPH-Based Free Surface Flows

Smoothed particle hydrodynamics (SPH) is efficient, mass preserving, and flexible in handling topological changes. However, sparsely sampled thin features are difficult to simulate in SPH-based free surface flows, due to a number of robustness and stability issues. In this article, we address this problem from two perspectives: the robustness of surface forces and the numerical instability of thin features. We present a new surface tension force scheme based on a free surface energy functional, under the diffuse interface model. We develop an efficient way to calculate the air pressure force for free surface flows, without using air particles. Compared with previous surface force formulae, our formulae are more robust against particle sparsity in thin feature cases. To avoid numerical instability on thin features, we propose to adjust the internal pressure force by estimating the internal pressure at two scales and filtering the force using a geometry-aware anisotropic kernel. Our result demonstrates the effectiveness of our algorithms in handling a variety of sparsely sampled thin liquid features, including thin sheets, thin jets, and water splashes.