Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deforming fluid domains within the finite element method: Five
  mesh-based tracking methods in comparison   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.

30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat