Simulation of two-fluid flows using a Finite Element/level set method. Application to bubbles and vesicle dynamics

TL;DR

This paper introduces a novel finite element and level set-based simulation framework for two-fluid flows, effectively modeling bubble dynamics and vesicle behaviors like tank treading and tumbling with high accuracy.

Contribution

The work develops an advanced finite element/level set method incorporating inextensibility constraints and high-order polynomials for improved two-fluid flow simulations involving bubbles and vesicles.

Findings

Successfully simulated bubble rising in viscous fluid.

Validated vesicle behaviors such as tank treading and tumbling.

Enhanced simulation accuracy with high-order polynomial approximation.

Abstract

A new framework for two-fluids flow using a Finite Element/Level Set method is presented and verified through the simulation of the rising of a bubble in a viscous fluid. This model is then enriched to deal with vesicles (which mimic red blood cells mechanical behavior) by introducing a Lagrange multiplier to constrain the inextensibility of the membrane. Moreover, high order polynomial approximation is used to increase the accuracy of the simulations. A validation of this model is finally presented on known behaviors of vesicles under flow such as "tank treading" and tumbling motions.