A numerical approach for fluid deformable surfaces with conserved enclosed volume
Abstract
We consider surface finite elements and a semi-implicit time stepping scheme to simulate fluid deformable surfaces. Such surfaces are modeled by incompressible surface Navier-Stokes equations with bending forces. Here, we consider closed surfaces and enforce conservation of the enclosed volume. The numerical approach builds on higher order surface parameterizations, a Taylor-Hood element for the surface Navier-Stokes part, appropriate approximations of the geometric quantities of the surface mesh redistribution and a Lagrange multiplier for the constraint. The considered computational examples highlight the solid-fluid duality of fluid deformable surfaces and demonstrate convergence properties that are known to be optimal for different sub-problems.
Cite
@article{arxiv.2210.03585,
title = {A numerical approach for fluid deformable surfaces with conserved enclosed volume},
author = {Veit Krause and Axel Voigt},
journal= {arXiv preprint arXiv:2210.03585},
year = {2023}
}