  In this work, we present a family of time and space high order finite volume
schemes for the solution of the full Boltzmann equation. The velocity space is
approximated by using a discrete ordinate approach while the collisional
integral is solved by spectral methods. The space reconstruction is realized by
integrating the distribution function, describing the state of the system, over
arbitrary shaped and closed control volumes using a Central Weighted ENO
(CWENO) technique. Compared to other reconstruction methods, this approach
permits to keep compact stencil sizes which is a remarkable property in the
context of kinetic equations due to the considerable demand of computational
resources. The full discretization is then obtained by combining the previous
phase-space approximation with high order Implicit-Explicit (IMEX) Runge Kutta
schemes. These methods guarantee stability, accuracy and preservation of the
asymptotic state. Comparisons of the Boltzmann model with simpler relaxation
type kinetic models (like BGK) is proposed showing the capability of the
Boltzmann equation to capture different physical solutions. The theoretical
order of convergence is numerically measured in different regimes and the
methods are tested on several standard two-dimensional benchmark problems in
comparison with Direct Simulation Monte Carlo results. The article ends with a
prototype engineering problem consisting of a subsonic and a supersonic flow
around a NACA 0012 airfoil. All test cases are run with MPI parallelization on
several threads, thus making the proposed methods suitable for parallel
distributed memory supercomputers.
