The goal of this review paper is to provide the reader with a concise introduction to the
mathematical theory of collision processes in (dilute) gases and plasmas, viewed as a …

This article reviews rarefied gas flow computations based on nonlinear model Boltzmann
equations using deterministic high-order gas-kinetic unified algorithms (GKUA) in phase …

In this survey we consider the development and mathematical analysis of numerical
methods for kinetic partial differential equations. Kinetic equations represent a way of …

In this paper we show that the use of spectral Galerkin methods for the approximation of the
Boltzmann equation in the velocity space permits one to obtain spectrally accurate …

The Boltzmann equation describes the dynamics of rarefied gas flows, but the
multidimensional nature of its collision operator poses a real challenge for its numerical …

The development of accurate and fast numerical schemes for the five-fold Boltzmann
collision integral represents a challenging problem in scientific computing. For a particular …

We present an abstract method for deriving decay estimates on the resolvents and
semigroups of non-symmetric operators in Banach spaces in terms of estimates in another …

In [C. Mouhot and L. Pareschi," Fast algorithms for computing the Boltzmann collision
operator," Math. Comp., to appear; C. Mouhot and L. Pareschi, CR Math. Acad. Sci. Paris …

We derive a conservative multispecies BGK model that follows the spirit of the original,
single species BGK model by making the specific choice to conserve species masses, total …

We propose a simple fast spectral method for the Boltzmann collision operator with general
collision kernels. In contrast to the direct spectral method L. Pareschi and G. Russo, SIAM J …