Modeling and Simulation of Open Membranes in Stokes Flow with Mixed-Dimensional Coupling
arXiv:2504.16823 · doi:10.1137/25M1762476
The paper introduces a mathematical and computational framework that couples three‑dimensional Stokes flow, a two‑dimensional lipid bilayer membrane, and its one‑dimensional free edge, using an axisymmetric hybrid BEM‑FEM method with local mesh refinement to resolve edge singularities.
Abstract
In this work, we present a mathematical and computational framework to model the dynamics of open lipid bilayer membranes interacting with ambient Stokes flow. The model explicitly couples the three-dimensional viscous fluid, the two-dimensional membrane surface, and its one-dimensional free edge. We develop an axisymmetric hybrid BEM-FEM method that solves the problem with an effective one-dimensional formulation. A key component is a local mesh refinement strategy designed to accurately resolve singularities and boundary layers originating at the membrane edge. Several numerical examples are provided to showcase its ability to capture intricate edge dynamics and multiscale fluid-membrane coupling.