Deforming fluid domains within the finite element method: Five mesh-based tracking methods in comparison
For researchers in computational fluid dynamics, this is an incremental review that organizes existing methods without introducing new results or comparisons.
This paper reviews five mesh-based tracking methods for deforming fluid domains in finite element simulations, covering interface tracking and capturing techniques. It discusses their history, recent developments including XFEM and IGA, and illustrates challenges in two-phase flow and sloshing tank applications.
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.