Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Advection improves homogenized models of continuum diffusion in
  one-dimensional heterogeneous media   We propose an alternative method for one-dimensional continuum diffusion
models with spatially variable (heterogeneous) diffusivity. Our method, which
extends recent work on stochastic diffusion, assumes the constant-coefficient
homogenized equation takes the form of an advection-diffusion equation with
effective (diffusivity and velocity) coefficients. To calculate the effective
coefficients, our approach involves solving two uncoupled boundary value
problems over the heterogeneous medium and leads to coefficients depending on
the spatially-varying diffusivity (as usual) as well as the boundary conditions
imposed on the heterogeneous model. Computational experiments comparing our
advection-diffusion homogenized model to the standard homogenized model
demonstrate that including an advection term in the homogenized equation leads
to improved approximations of the solution of the original heterogeneous model.

31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ