Thin-feature-aware transport-velocity formulation for SPH-based liquid animation

Realistic liquid animations with thin sheets or streams are crucial for creating fluid effects in digital media. However, it is challenging to simulate these appealing thin sheets or streams in the framework of smoothed particle hydrodynamics (SPH). The underlying reason for this challenge mainly lies in the inherent numerical instability of SPH due to inconsistent kernel interpolation, which is caused by the incomplete kernel support on the free surface and the particles' disorder dispersion within the simulation domain. To address this challenge, we propose a novel and effective approach to ensure the consistency of kernel interpolation at both internal flow and the free surface during the simulation such that these thin features can always be well maintained. First, we introduce a transport-velocity formulation to alleviate the disorder dispersion in the liquid domain. However, this formulation can only work in the internal flow, and it fails at the free surface because it cannot accurately estimate the density of particles there. To this end, we propose adaptively correcting the underestimated density caused by the incomplete kernel support of free-surface particles, which are identified by a geometry-aware anisotropic kernel, to counteract the inconsistent interpolation on the free surface. Then, we propose a novel scheme to further filter the background pressure to enhance the interactions between the internal flow and the free surface, as well as liquid and solid, such that the thin features generated from such interactions can be realistically simulated. The proposed approach can also achieve anticlumping and regularization effects in the entire simulation domain and, hence, further enhance the thin features in liquids. We evaluate our method on a variety of benchmark examples, and the results demonstrate that our method can achieve more appealing visual effects than state-of-the-art methods by realistically simulating more vivid thin features.