Date of Award

Winter 2023

Document Type

Thesis (Master's)

Department or Program

Computer Science

First Advisor

Prof. Bo Zhu


In this thesis, we introduce a Moving Eulerian-Lagrangian Particle (MELP) method, a mesh-free method to simulate incompressible thin-film fluid systems: soap bubbles, bubble clusters, and foams. The realistic simulation of such systems depends upon the successful treatment of three aspects: (1) the soap film's deformation due to the tendency to minimize the surface energy, giving rise to the bouncy characteristics of soap bubbles, (2) the tangential fluid flow on the thin film, causing the thickness to vary spatially, which in conjunction with thin-film interference creates evolving and highly sophisticated iridescent color patterns, (3) the topological changes due to collision, separation, and fragmentation, which may create partition surfaces and non-manifold junctions that spontaneously settle into honeycomb structures due to force balance. The interleaving complexities from all three fronts render the task of accurately and affordably simulating thin-film fluid an open problem for the Computational Physics and Computer Graphics community. The proposed MELP method tackles these multifaceted challenges by employing a novel, bi-layer particle structure: a sparse set of Eulerian particles for dynamic interface tracking and PDE solving, and a fine set of Lagrangian particles for material and momentum transport. Such a design provides crucially advantageous numerical traits compared to existing frameworks. Compared to mesh-based methods, MELP's particle-based nature makes it topologically agnostic, which allows it to conveniently simulate topological changes such as bubble-cluster formation and thin-film rupture. Furthermore, these Lagrangian structures carry out fluid advection naturally, conserve mass by design, and track "sub-grid" flow details. Compared to existing particle methods, our bi-layer design improves drastically on the computational performance in terms of both stability and efficiency. The advantage of this design will manifest in a wide range of experiments, including dynamic foam formation, Rayleigh-Taylor instability, Newton Black Films, and bubble bursting, showing an increased level of flow detail, increased number of regions in bubble clusters, and increased flexibility to recreate multi-junction formation on-the-fly. Furthermore, we validate its physical correctness against a variety of analytical baselines, by successfully recovering the equilibrium dihedral and tetrahedral angles, the exponential thickness profile of drainage under gravity, the curvature of partition surfaces, and the minimum surface area of double-bubbles.

Original Citation

Deng, Yitong, et al. "A moving eulerian-lagrangian particle method for thin film and foam simulation." ACM Transactions on Graphics (TOG) 41.4 (2022): 1-17.