A review of mathematical topics in collisional kinetic theory
C Villani - Handbook of mathematical fluid dynamics, 2002 - books.google.com
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 …
mathematical theory of collision processes in (dilute) gases and plasmas, viewed as a …
Rarefied gas flow simulations using high-order gas-kinetic unified algorithms for Boltzmann model equations
ZH Li, AP Peng, HX Zhang, JY Yang - Progress in Aerospace Sciences, 2015 - Elsevier
This article reviews rarefied gas flow computations based on nonlinear model Boltzmann
equations using deterministic high-order gas-kinetic unified algorithms (GKUA) in phase …
equations using deterministic high-order gas-kinetic unified algorithms (GKUA) in phase …
Numerical methods for kinetic equations
G Dimarco, L Pareschi - Acta Numerica, 2014 - cambridge.org
In this survey we consider the development and mathematical analysis of numerical
methods for kinetic partial differential equations. Kinetic equations represent a way of …
methods for kinetic partial differential equations. Kinetic equations represent a way of …
A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources
In this paper, we propose a general time-discrete framework to design asymptotic-
preserving schemes for initial value problem of the Boltzmann kinetic and related equations …
preserving schemes for initial value problem of the Boltzmann kinetic and related equations …
Deterministic numerical solutions of the Boltzmann equation using the fast spectral method
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 …
multidimensional nature of its collision operator poses a real challenge for its numerical …
Implicit–explicit schemes for BGK kinetic equations
S Pieraccini, G Puppo - Journal of Scientific Computing, 2007 - Springer
In this work a new class of numerical methods for the BGK model of kinetic equations is
presented. In principle, schemes of any order of accuracy in both space and time can be …
presented. In principle, schemes of any order of accuracy in both space and time can be …
Fast algorithms for computing the Boltzmann collision operator
C Mouhot, L Pareschi - Mathematics of computation, 2006 - ams.org
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 …
collision integral represents a challenging problem in scientific computing. For a particular …
[HTML][HTML] Boltzmann's equation at 150: Traditional and modern solution techniques for charged particles in neutral gases
Seminal gas discharge experiments of the late 19th and early 20th centuries laid the
foundations of modern physics, and the influence of this “golden era” continues to resonate …
foundations of modern physics, and the influence of this “golden era” continues to resonate …
Solving the Boltzmann equation deterministically by the fast spectral method: application to gas microflows
Based on the fast spectral approximation to the Boltzmann collision operator, we present an
accurate and efficient deterministic numerical method for solving the Boltzmann equation …
accurate and efficient deterministic numerical method for solving the Boltzmann equation …
A conservative, entropic multispecies BGK model
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 …
single species BGK model by making the specific choice to conserve species masses, total …