[SMaLS] Geometry and Mechanics of Fluid Surfaces

Speaker: Cuncheng Zhu, UC San Diego, Saintillan Group

Title: Geometry and Mechanics of Fluid Surfaces

Abstract: This talk focuses on the computational and geometric modeling of dissipative fluid mechanics on general surfaces, motivated by applications in biophysics. Drawing on differential-geometric continuum mechanics and variational principles, I present a unified framework for describing fluid dynamics on curved and evolving surfaces, and show how geometry and topology affect fluid motion and shape dynamics. This framework applies to active nematic surfaces, as well as classical limits such as Navier–Stokes vortex dynamics and Helfrich-Stokes relaxation.
I show how geometric abstraction — through coordinate invariance and variational principles — clarifies the mathematical structure of fluid surfaces and provides a systematic way for deriving and understanding governing equations with increasing complexity. By translating the continuous structures into structure-preserving discrete formulations, we address long-standing challenges in numerical PDEs and provide new computational tools for studying biophysical questions about shape and form emerging from self-organized flows.