Functional Thin Films on Surfaces.

Area of Science:

• Computational fluid dynamics
• Geometric partial differential equations
• Computer graphics

Background:

• Simulating thin viscous fluid films on curved surfaces is computationally challenging.
• Existing methods struggle with intricate visual phenomena and geometric complexities.
• Reduced models focusing on mass density evolution are difficult to discretize due to high-order nonlinear PDEs.

Purpose of the Study:

• To develop a novel numerical model for simulating thin viscous fluid films on triangle meshes.
• To adapt a variational formulation for smooth surfaces to discrete mesh representations.
• To enable efficient and stable simulation of complex fluid behaviors on curved surfaces.

Main Methods:

• Developed a discretization for curvature and advection operators on triangle meshes.
• Employed a variational approach inspired by smooth surface formulations.
• Implemented a numerical scheme requiring a single sparse linear solve per time step.
• Ensured exact preservation of total fluid volume.

Main Results:

• The proposed method is efficient and stable for simulating fluid film dynamics.
• It accurately reproduces known phenomena like droplet formation, evaporation, and viscous fingering.
• The model successfully incorporates van der Waals forces, enabling effects like pearling.

Conclusions:

• The presented method offers an effective approach for simulating thin viscous films on complex geometries.
• It overcomes discretization challenges of high-order PDEs on meshes.
• The model's ability to preserve volume and capture intricate effects makes it valuable for research and applications.