Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simulation of incompressible two-phase flow in porous media with large
  timesteps   Multiphase flow in porous media occurs in several disciplines including
petroleum reservoir engineering, petroleum systems' analysis, and CO$_2$
sequestration. While simulations often use a fully implicit discretization to
increase the time step size, restrictions on the time step often exist due to
non-convergence of the nonlinear solver (e.g. Newton's method). Here this
problem is addressed for the Buckley-Leverett equations, which model
incompressible, immiscible, two-phase flow with no capillary potential. The
equations are recast as a gradient flow using the phase-field method, and a
convex energy splitting scheme is applied to enable large timesteps, even for
high degrees of heterogeneity in permeability and viscosity. By using the
phase-field formulation as a homotopy map, the underlying hyperbolic flow
equations can be solved with large timesteps. For a heterogeneous test problem,
the new homotopy method allows the timestep to be increased by more than six
orders of magnitude relative to the unmodified equations while maintaining
convergence.

30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math