An asymptotic preserving scheme for the Kac model of the Boltzmann equation in the diffusion limit

Continuum Mechanics and Thermodynamics ◽

10.1007/s00161-009-0116-2 ◽

2009 ◽

Vol 21 (5) ◽

pp. 401-421 ◽

Author(s):

Mounir Bennoune ◽

Mohammed Lemou ◽

Luc Mieussens

Keyword(s):

Boltzmann Equation ◽

Diffusion Limit ◽

Asymptotic Preserving ◽

The Boltzmann Equation ◽

Kac Model ◽

Asymptotic Preserving Scheme

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An Asymptotic Preserving Scheme for the ES-BGK Model of the Boltzmann Equation

Journal of Scientific Computing ◽

10.1007/s10915-010-9394-x ◽

2010 ◽

Vol 46 (2) ◽

pp. 204-224 ◽

Author(s):

Francis Filbet ◽

Shi Jin

Keyword(s):

Boltzmann Equation ◽

Bgk Model ◽

Asymptotic Preserving ◽

The Boltzmann Equation ◽

Asymptotic Preserving Scheme

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A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit

SIAM Journal on Scientific Computing ◽

10.1137/07069479x ◽

2008 ◽

Vol 31 (1) ◽

pp. 334-368 ◽

Author(s):

Mohammed Lemou ◽

Luc Mieussens

Keyword(s):

Kinetic Equations ◽

Diffusion Limit ◽

Asymptotic Preserving ◽

Asymptotic Preserving Scheme ◽

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An asymptotic-preserving Monte Carlo method for the Boltzmann equation

Journal of Computational Physics ◽

10.1016/j.jcp.2014.07.029 ◽

2014 ◽

Vol 276 ◽

pp. 380-404 ◽

Author(s):

Wei Ren ◽

Hong Liu ◽

Shi Jin

Keyword(s):

Monte Carlo ◽

Boltzmann Equation ◽

Monte Carlo Method ◽

Asymptotic Preserving ◽

The Boltzmann Equation

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An asymptotic-preserving scheme for the semiconductor Boltzmann equation with two-scale collisions: A splitting approach

Kinetic and Related Models ◽

10.3934/krm.2015.8.707 ◽

2015 ◽

Vol 8 (4) ◽

pp. 707-723 ◽

Author(s):

Jingwei Hu ◽

Shi Jin ◽

Li Wang

Keyword(s):

Boltzmann Equation ◽

Asymptotic Preserving ◽

Semiconductor Boltzmann Equation ◽

Asymptotic Preserving Scheme

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Particle simulations of the Kac model of the Boltzmann equation

Journal of Computational and Applied Mathematics ◽

10.1016/s0377-0427(97)00184-2 ◽

1997 ◽

Vol 87 (1) ◽

pp. 169-193 ◽

Author(s):

Ibrahim Coulibaly ◽

Christian Lécot

Keyword(s):

Boltzmann Equation ◽

The Boltzmann Equation ◽

Kac Model ◽

Particle Simulations

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A BGK-penalization-based asymptotic-preserving scheme for the multispecies Boltzmann equation

Numerical Methods for Partial Differential Equations ◽

10.1002/num.21746 ◽

2012 ◽

Vol 29 (3) ◽

pp. 1056-1080 ◽

Author(s):

Shi Jin ◽

Qin Li

Keyword(s):

Boltzmann Equation ◽

Asymptotic Preserving ◽

Asymptotic Preserving Scheme

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Exact solution for the spatially inhomogeneous nonlinear Kac model of the Boltzmann equation

Journal of Mathematical Physics ◽

10.1063/1.526526 ◽

1985 ◽

Vol 26 (6) ◽

pp. 1203-1214 ◽

Author(s):

Henri Cornille

Keyword(s):

Exact Solution ◽

Boltzmann Equation ◽

Spatially Inhomogeneous ◽

The Boltzmann Equation ◽

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Asymptotic preserving Monte Carlo methods for the Boltzmann equation

Transport Theory and Statistical Physics ◽

10.1080/00411450008205882 ◽

2000 ◽

Vol 29 (3-5) ◽

pp. 415-430 ◽

Author(s):

L. Pareschi ◽

G. Russo

Keyword(s):

Monte Carlo ◽

Boltzmann Equation ◽

Monte Carlo Methods ◽

Asymptotic Preserving ◽

The Boltzmann Equation

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An asymptotic-preserving scheme for the semiconductor Boltzmann equation toward the energy-transport limit

Journal of Computational Physics ◽

10.1016/j.jcp.2014.10.050 ◽

2015 ◽

Vol 281 ◽

pp. 806-824 ◽

Author(s):

Jingwei Hu ◽

Li Wang

Keyword(s):

Boltzmann Equation ◽

Energy Transport ◽

Asymptotic Preserving ◽

Semiconductor Boltzmann Equation ◽

Asymptotic Preserving Scheme

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Analysis of an Asymptotic Preserving Scheme for Stochastic Linear Kinetic Equations in the Diffusion Limit

SIAM/ASA Journal on Uncertainty Quantification ◽

10.1137/18m1175641 ◽

2019 ◽

Vol 7 (2) ◽

pp. 760-785

Author(s):

Nathalie Ayi ◽

Erwan Faou

Keyword(s):

Kinetic Equations ◽

Diffusion Limit ◽

Asymptotic Preserving ◽

Asymptotic Preserving Scheme ◽

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