Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Energy-Stable Scheme for Incompressible Navier-Stokes Equations with
  Periodically Updated Coefficient Matrix   We present an energy-stable scheme for simulating the incompressible
Navier-Stokes equations based on the generalized Positive Auxiliary Variable
(gPAV) framework. In the gPAV-reformulated system the original nonlinear term
is replaced by a linear term plus a correction term, where the correction term
is put under control by an auxiliary variable. The proposed scheme incorporates
a pressure-correction type strategy into the gPAV procedure, and it satisfies a
discrete energy stability property. The scheme entails the computation of two
copies of the velocity and pressure within a time step, by solving an
individual de-coupled linear equation for each of these field variables. Upon
discretization the pressure linear system involves a constant coefficient
matrix that can be pre-computed, while the velocity linear system involves a
coefficient matrix that is updated periodically, once every $k_0$ time steps in
the current work, where $k_0$ is a user-specified integer. The auxiliary
variable, being a scalar-valued number, is computed by a well-defined explicit
formula, which guarantees the positivity of its computed values. It is observed
that the current method can produce accurate simulation results at large (or
fairly large) time step sizes for the incompressible Navier-Stokes equations.
The impact of the periodic coefficient-matrix update on the overall cost of the
method is observed to be small in typical numerical simulations. Several flow
problems have been simulated to demonstrate the accuracy and performance of the
method developed herein.

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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
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The categories of this paper are: econ
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: eess