GARM-LS: A Gradient-Augmented Reference-Map Method for Level-Set Fluid Simulation

This paper presents a novel level-set method that combines gradient augmentation and reference mapping to enable high-fidelity interface tracking and surface tension flow simulation, preserving small-scale volumes and interface features comparable to the grid size. At the center of our approach is a novel reference-map algorithm to concurrently convect level-set values and gradients, both of which are crucial for reconstructing a dynamic surface exhibiting small-scale volumes. In addition, we develop a full pipeline for the new level-set scheme by incorporating a novel extrapolation algorithm and an enhanced reinitialization procedure into our reference-map method. We test our algorithm by simulating complex surface tension flow phenomena such as raindrop collision, merging, and splashing. We also showcase the efficacy of our approach by performing validation tests and comparing it to a broad range of existing level-set algorithms.