Author ORCID Identifier

Date of Award

Spring 5-8-2024

Document Type

Thesis (Ph.D.)

Department or Program

Computer Science

First Advisor

Bo Zhu


Solid-fluid interactions are ubiquitous in nature, and accurate simulation methods are essential for realistic animation, industrial design, and engineering analysis. Com- pared to large-scale coupling phenomena, simulating fine-scale interactions poses extra challenges due to factors such as surface tension, material wettability, and geometric complexity. In this thesis, we pursue novel methodologies to accurately model in- terfacial dynamics between surface-tension fluids and codimensional solids, involving capillary interactions, controllable wettability, and robust contact behaviors. Our ini- tial approach involves developing a novel three-way coupling method, which utilizes a thin liquid membrane, modelled as a simplicial mesh, to facilitate accurate momen- tum transfer, collision processing, and surface stress calculation. We further devise a monolithic solver and an implicit Newmark scheme to solve the interactions among the three systems of liquid, solid, and membrane. We demonstrate the efficacy of our method through an array of rigid-fluid contact simulations dominated by strong surface tension, such as the surface-tension-driven support of high-density objects, ”Cheerios effect” where floating objects attracting one another, and surface tension weakening effect caused by surface-active constituents. Next, we complement our method by accounting for the wettability of solid surfaces. The central component is a Lagrangian model that tackles the coupling, evolution, and equilibrium of dynamic contact lines evolving on the interface between surface-tension fluid and deformable objects. This model captures an ensemble of small-scale geometric and physical processes, including dynamic water-front tracking, local momentum transfer and force balance, and interfacial stress calculation. On top of this contact-line model, we fur- ther developed a mesh-based level set method to evolve the three-phase T-junction on a deformable solid surface. Our dynamic contact-line model, in conjunction with its monolithic coupling system, unifies the treatment of hydrophobic and hydrophilic solid-fluid-interaction and enables a broad range of challenging small-scale elastocap- illary phenomena that were previously impractical to solve. Lastly, we investigate collision and contact between Eulerian fluids and thin elastic solids such as shells and rods, whose geometries are difficult to represent accurately on a fixed Eulerian grid. We reformulate the contact process as an optimization system augmented with barriers, which aims to find a configuration that ensures the absence of penetration while enforcing incompressibility for the fluids and minimizing elastic potentials for the solids. By integrating the inertia, solid elastic potential, damping, barrier po- tential, and fluid incompressibility within a unified system, we are able to robustly simulate a wide range of processes involving fluid interactions with lower-dimensional objects such as shells and rods. These processes include topology changes, bouncing, splashing, sliding, rolling, floating, and more.