  We propose a particle-based method to simulate thin-film fluid that jointly
facilitates aggressive surface deformation and vigorous tangential flows. We
build our dynamics model from the surface tension driven Navier-Stokes equation
with the dimensionality reduced using the asymptotic lubrication theory and
customize a set of differential operators based on the weakly compressible
Smoothed Particle Hydrodynamics (SPH) for evolving pointset surfaces. The key
insight is that the compressible nature of SPH, which is unfavorable in its
typical usage, is helpful in our application to co-evolve the thickness,
calculate the surface tension, and enforce the fluid incompressibility on a
thin film. In this way, we are able to two-way couple the surface deformation
with the in-plane flows in a physically based manner. We can simulate complex
vortical swirls, fingering effects due to Rayleigh-Taylor instability,
capillary waves, Newton's interference fringes, and the Marangoni effect on
liberally deforming surfaces by presenting both realistic visual results and
numerical validations. The particle-based nature of our system also enables it
to conveniently handle topology changes and codimension transitions, allowing
us to marry the thin-film simulation with a wide gamut of 3D phenomena, such as
pinch-off of unstable catenoids, dripping under gravity, merging of droplets,
as well as bubble rupture.
