Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Riemann solvers and pressure gradients in Godunov-type schemes for
  variable density incompressible flows   Variable density incompressible flows are governed by parabolic equations.
The artificial compressibility method makes these equations hyperbolic-type,
which means that they can be solved using techniques developed for compressible
flows, such as Godunov-type schemes. While the artificial compressibility
method is well-established, its application to variable density flows has been
largely neglected in the literature. This paper harnesses recent advances in
the wider field by applying a more robust Riemann solver and a more easily
parallelisable time discretisation to the variable density equations than
previously. We also develop a new method for calculating the pressure gradient
as part of the second-order reconstruction step. Based on a rearrangement of
the momentum equation and an exploitation of the other gradients and source
terms, the new pressure gradient calculation automatically captures the
pressure gradient discontinuity at the free surface. Benchmark tests
demonstrate the improvements gained by this robust Riemann solver and new
pressure gradient calculation.

31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph