Modeling and Simulation of Open Membranes in Stokes Flow with Mixed-Dimensional Coupling
This work provides a new computational tool for biophysicists studying membrane dynamics, but the method is axisymmetric and the results are qualitative, limiting immediate impact.
The authors developed a computational framework for modeling open lipid bilayer membranes in Stokes flow, coupling 3D fluid, 2D membrane, and 1D edge dynamics. Their axisymmetric hybrid BEM-FEM method with local mesh refinement captures intricate edge dynamics and multiscale coupling.
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.