Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A boundary matching micro/macro decomposition for kinetic equations   We introduce a new micro/macro decomposition of collisional kinetic equations
which naturally incorporates the exact space boundary conditions. The idea is
to write the distribution fonction $f$ in all its domain as the sum of a
Maxwellian adapted to the boundary (which is not the usual Maxwellian
associated with $f$) and a reminder kinetic part. This Maxwellian is defined
such that its 'incoming' velocity moments coincide with the 'incoming' velocity
moments of the distribution function. Important consequences of this strategy
are the following. i) No artificial boundary condition is needed in the
micro/macro models and the exact boundary condition on $f$ is naturally
transposed to the macro part of the model. ii) It provides a new class of the
so-called 'Asymptotic preserving' (AP) numerical schemes: such schemes are
consistent with the original kinetic equation for all fixed positive value of
the Knudsen number $\eps$, and if $\eps \to 0 $ with fixed numerical parameters
then these schemes degenerate into consistent numerical schemes for the various
corresponding asymptotic fluid or diffusive models. Here, the strategy provides
AP schemes not only inside the physical domain but also in the space boundary
layers. We provide a numerical test in the case of a diffusion limit of the
one-group transport equation, and show that our AP scheme recovers the boundary
layer and a good approximation of the theoretical boundary value, which is
usually computed from to the so-called Chandrasekhar function.

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The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga