Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fully Implicit Multidimensional Hybrid Upwind Scheme for Coupled Flow
  and Transport   Robust and accurate fully implicit finite-volume schemes applied to
Darcy-scale multiphase flow and transport in porous media are highly desirable.
Recently, a smooth approximation of the saturation-dependent flux coefficients
based on Implicit Hybrid Upwinding (IHU) has been proposed to improve the
nonlinear convergence in fully implicit simulations with buoyancy. Here, we
design a truly multidimensional extension of this approach that retains the
simplicity and robustness of IHU while reducing the sensitivity of the results
to the orientation of the computational (Cartesian) grid. This is achieved with
the introduction of an adaptive, local coupling between the fluxes that takes
the flow pattern into account. We analyze the mathematical properties of the
proposed methodology to show that the scheme is monotone in the presence of
competing viscous and buoyancy forces and yields saturations remaining between
physical bounds. Finally, we demonstrate the efficiency and accuracy of the
scheme on challenging two-dimensional two-phase examples with buoyancy, with an
emphasis on the reduction of the grid orientation effect.

33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph