Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On numerical stabilization in modeling double-diffusive viscous
  fingering   A firm understanding and control of viscous fingering (VF) and miscible
displacement will be vital to a wide range of industrial, environmental, and
pharmaceutical applications, such as geological carbon-dioxide sequestration,
enhanced oil recovery, and drug delivery. We restrict our study to VF, a
well-known hydrodynamic instability, in miscible fluid systems but consider
double-diffusive (DD) effects---the combined effect of compositional changes
because of solute transport and temperature. One often uses numerical
formulations to study VF with DD effects. The primary aim of the current study
is to show that popular formulations have limitations to study VF with DD
effect. These limitations include exhibiting node-to-node spurious
oscillations, violating physical constraints such as the non-negativity of the
concentration field or mathematical principles such as the maximum principle,
and suppressing physical instabilities. We will use several popular stabilized
finite element formulations---the SUPG formulations and three modifications
based on the SOLD approach---in our study. Using representative numerical
results, we will illustrate two critical limitations. First, we document that
these formulations do not respect the non-negative constraint and the maximum
principle for the concentration field. We will also show the impact of these
violations on how viscous fingers develop. Second, we show that these
stabilized formulations, often used to suppress numerical instabilities, may
also suppress physical instabilities, such as viscous fingering. Our study will
be valuable to practitioners who use existing numerical formulations and to
computational mathematicians who develop new formulations.

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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph