Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A consistent discretization of the single-field two-phase momentum
  convection term for the unstructured finite volume Level Set / Front Tracking
  method   We propose the rhoLENT method, an extension of the unstructured Level Set /
Front Tracking (LENT) method, based on the collocated Finite Volume equation
discretization, that recovers exact numerical stability for the two-phase
momentum convection with a range of density ratios, namely $\rho^-/\rho^+\in
[1, 10000]$. We provide the theoretical basis for the numerical inconsistency
in the collocated finite volume equation discretization of the single-field
two-phase momentum convection. The cause of the numerical inconsistency lies in
the way the cell-centered density is computed in the new time step
($\rho_c^{n+1}$). Specifically, if $\rho_c^{n+1}$ is computed from the
approximation of the fluid interface at $t^{n+1}$, and it is not computed by
solving a mass conservation equation (or its equivalent), the two-phase
momentum convection term will automatically be inconsistently discretized. We
provide the theoretical justification behind using the auxiliary mass
conservation equation to stabilize flows with strong density ratios. The
evaluation of the face-centered (mass flux) density we base on the fundamental
principle of mass conservation, used to model the single-field density,
contrary to the use of different weighted averages of cell-centered
single-field densities and alternative reconstructions of the mass flux density
by other contemporary methods. Implicit discretization of the two-phase
momentum convection term is achieved, removing the CFL stability criterion.
Numerical stability is demonstrated in terms of the relative $L_\infty$
velocity error norm with realistic viscosity and strong surface tension forces.
The stabilization technique in the rhoLENT method is also applicable to other
two-phase flow simulation methods that utilize the collocated unstructured
Finite Volume Method to discretize single-field two-phase Navier-Stokes
Equations.

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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: stat
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: math
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The categories of this paper are: q-bio