Deforming fluid domains within the finite element method: Five mesh-based tracking methods in comparison

TL;DR

This paper compares five mesh-based methods for tracking deforming fluid domains in free-surface flow simulations, highlighting recent advances and addressing key challenges like surface representation and surface tension effects.

Contribution

It provides a comprehensive review and comparison of five different mesh-based domain tracking methods, including recent developments like XFEM and IGA, for free-surface flow applications.

Findings

Level-set and volume-of-fluid methods effectively capture interface dynamics.

Extended finite elements improve interface representation accuracy.

NURBS-based methods enhance geometric fidelity in simulations.

Abstract

Fluid flow applications can involve a number of coupled problems. One is the simulation of free-surface flows, which require the solution of a free-boundary problem. Within this problem, the governing equations of fluid flow are coupled with a domain deformation approach. This work reviews five of those approaches: interface tracking using a boundary-conforming mesh and, in the interface capturing context, the level-set method, the volume-of-fluid method, particle methods, as well as the phase-field method. The history of each method is presented in combination with the most recent developments in the field. Particularly, the topics of extended finite elements (XFEM) and NURBS-based methods, such as Isogeometric Analysis (IGA), are addressed. For illustration purposes, two applications have been chosen: two-phase flow involving drops or bubbles and sloshing tanks. The challenges of these applications, such as the geometrically correct representation of the free surface or the incorporation of surface tension forces, are discussed.