Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A semi-discrete Boltzmann equation based on a finite volume scheme   In this work we consider the classical non-linear Boltzmann equation, where
the unknown is the distribution function $f$, which depends on the time $t$,
the vector $\mathbf{x}$ (the position of a molecule) and its velocity
$\mathbf{\xi}$. From the Boltzmann equation we derive a semi-discrete model,
which consists in a set of partial differential equations in time and space.
The new unknowns are two moments of the distribution function $f$ and,
according to a finite volume scheme, integrals of $f$ with respect to the
velocity $\mathbf{\xi}$, over bounded and open sets. We do not introduce any
approximation for the partial derivatives with respect to $\mathbf{x}$ and the
time $t$. We also propose the use of truncated octahedra as bounded domains of
integration. This reduces both the computing complexity and the number of the
constant numerical coefficients arising from the collision operator. All the
numerical parameters can be obtained by means of numerical quadrature.

4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin