A numerical approach for fluid deformable surfaces with conserved enclosed volume

TL;DR

This paper presents a numerical method using surface finite elements and semi-implicit time stepping to simulate fluid deformable surfaces with conserved volume, incorporating higher order parameterizations and a Lagrange multiplier.

Contribution

It introduces a novel numerical approach combining advanced surface discretization, a volume conservation constraint, and a semi-implicit scheme for simulating fluid deformable surfaces.

Findings

Demonstrates convergence properties of the method

Highlights the solid-fluid duality in simulations

Validates the approach with computational examples

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.