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Deforming Fluid Domains Within the Finite Element Method: Five Mesh-Based Tracking Methods in Comparison

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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 and NURBS-based methods, such as isogeometric analysis, 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.

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Acknowledgments

The authors gratefully acknowledge support from the German Research Foundation (DFG) through the SFB 1120 “Thermal Precision”, the Emmy-Noether-research group “Numerical methods for discontinuities in continuum mechanics”, and the DFG program GSC 111 (AICES Graduate School). The computations were conducted on computing clusters provided by the Jülich Aachen Research Alliance (JARA). Furthermore, we would like to thank Philipp Knechtges for the infinite patience with which he shared his mathematical insight.

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Elgeti, S., Sauerland, H. Deforming Fluid Domains Within the Finite Element Method: Five Mesh-Based Tracking Methods in Comparison. Arch Computat Methods Eng 23, 323–361 (2016). https://doi.org/10.1007/s11831-015-9143-2

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