Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A numerical method for the quasi-incompressible
  Cahn-Hilliard-Navier-Stokes equations for variable density flows with a
  discrete energy law   In this paper, we investigate numerically a diffuse interface model for the
Navier-Stokes equation with fluid-fluid interface when the fluids have
different densities \cite{Lowengrub1998}. Under minor reformulation of the
system, we show that there is a continuous energy law underlying the system,
assuming that all variables have reasonable regularities. It is shown in the
literature that an energy law preserving method will perform better for
multiphase problems. Thus for the reformulated system, we design a $C^0$ finite
element method and a special temporal scheme where the energy law is preserved
at the discrete level. Such a discrete energy law (almost the same as the
continuous energy law) for this variable density two-phase flow model has never
been established before with $C^0$ finite element. A Newton's method is
introduced to linearise the highly non-linear system of our discretization
scheme. Some numerical experiments are carried out using the adaptive mesh to
investigate the scenario of coalescing and rising drops with differing density
ratio. The snapshots for the evolution of the interface together with the
adaptive mesh at different times are presented to show that the evolution,
including the break-up/pinch-off of the drop, can be handled smoothly by our
numerical scheme. The discrete energy functional for the system is examined to
show that the energy law at the discrete level is preserved by our scheme.

29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin