A brief review of numerical methods for collision operators

Keywords

Collision, Statistical physics, Boltzmann equation, Boltzmann constant, Physics

References

• Chapter 2 – A Review of Mathematical Topics in Collisional Kinetic TheoryCédric Villani — 2002
• Molecular Gas Dynamics and the Direct Simulation of Gas FlowsG. A. Bird — 1994
• The grazing collision limit for the Boltzmann–Lorentz modelChristophe Buet, Stéphane Cordier, Brigitte Lucquin‐Desreux — 2001
• The mathematical theory of dilute gasesCarlo Cercignani, Reinhard Illner, Mario Pulvirenti — 1994
• The Boltzmann equation and its applicationsCarlo Cercignani — 1988
• Lecture Notes on the Discretization of the Boltzmann EquationNicola Bellomo, Renée Gatignol — 2003
• The Gaussian-BGK model of Boltzmann equation with small Prandtl numberPierre Andries, Patrick Le Tallec, Jean-Philippe Perlat — 2000
• Méthode spectrale rapide pour l'équation de Fokker–Planck–LandauLorenzo Pareschi, Giovanni Russo, Giuseppe Toscani — 2000
• Boltzmann type schemes for gas dynamics and the entropy propertyBenoı̂t Perthame — 1990
• An entropy scheme for the Fokker-Planck collision operator of plasma kinetic theoryPierre Degond, Brigitte Lucquin‐Desreux — 1994
• The Asymptotic Diffusion Limit of Discretized Transport ProblemsEdward W. Larsen — 1992
• An asymptotic-preserving well-balanced scheme for the hyperbolic heat equationsLaurent Gosse, Giuseppe Toscani — 2002
• Convergence of Discrete-Velocity Schemes for the Boltzmann EquationSt x E phane Mischler — 1997
• Discretization of the Multiscale Semiconductor Boltzmann Equation by Diffusive Relaxation SchemesShi Jin, Lorenzo Pareschi — 2000
• Direct simulation scheme derived from the Boltzmann equation. I - Monocomponent gases. II - MulticomKenichi Nanbu — 1980
• An introduction to Monte Carlo method for the Boltzmann equationLorenzo Pareschi, Giovanni Russo — 2001
• Conservative and Entropy Decaying Numerical Scheme for the Isotropic Fokker-Planck-Landau EquationChristophe Buet, Stéphane Cordier — 1998
• Numerical Analysis of Conservative and Entropy Schemes for the Fokker--Planck--Landau EquationChristophe Buet, Stéphane Cordier — 1999
• On boltzmann equations and fokker—planck asymptotics: Influence of grazing collisionsThierry Goudon — 1997
• Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic EquationsShi Jin — 1999

Cited by

• Particle approximation of some Landau equationsNicolas Fournier, ,LAMA UMR 8050, Faculté de Sciences et Technologies, Université Paris Est, 61 avenue du Général de Gaulle, 94010 Créteil Cedex — 2008

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