Numerical Schemes for Kinetic Equations in the Anomalous Diffusion Limit. Part II: Degenerate Collision Frequency

DOI10.1137/15M1053190OpenAlexW2513869217MaRDI QIDQ2818243

Hélène Hivert, Nicolas Crouseilles, Mohammed Lemou

Publication date: 7 September 2016

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1053190

zbMATH Keywords

BGK equationfractional diffusion equationasymptotic preserving schemesanomalous diffusion limitdegenerate collision frequency

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Numerical methods for stiff equations (65L04) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items (8)

On a structure-preserving numerical method for fractional Fokker-Planck equations ⋮ Wave turbulence and thermalization in one-dimensional chains ⋮ Numerical schemes for kinetic equation with diffusion limit and anomalous time scale ⋮ An asymptotic preserving scheme for kinetic models with singular limit ⋮ An Asymptotic-Preserving Scheme for the Kinetic Equation with Anisotropic Scattering: Heavy Tail Equilibrium and Degenerate Collision Frequency ⋮ Numerical Schemes for Kinetic Equations in the Anomalous Diffusion Limit. Part I: The Case of Heavy-Tailed Equilibrium ⋮ Multiscale numerical schemes for kinetic equations in the anomalous diffusion limit ⋮ Fractional hypocoercivity

Cites Work

• Unnamed Item
• Numerical schemes for kinetic equations in diffusive regimes
• On the asymptotic preserving property of the unified gas kinetic scheme for the diffusion limit of linear kinetic models
• Fractional diffusion limit for collisional kinetic equations: a Hilbert expansion approach
• Anomalous energy transport in FPU-\(\beta\) chain
• Numerical schemes of diffusion asymptotics and moment closures for kinetic equations
• Fractional diffusion limit for collisional kinetic equations
• An asymptotic-preserving scheme for linear kinetic equation with fractional diffusion limit
• Boltzmann equations for mixtures of Maxwell gases: exact solutions and power like tails
• Limit theorems for additive functionals of a Markov chain
• Boundary layers and homogenization of transport processes
• Scaling solutions of inelastic Boltzmann equations with over-populated high energy tails
• On some properties of kinetic and hydrodynamic equations for inelastic interactions.
• Multiscale numerical schemes for kinetic equations in the anomalous diffusion limit
• Numerical Schemes for Kinetic Equations in the Anomalous Diffusion Limit. Part I: The Case of Heavy-Tailed Equilibrium
• ANOMALOUS DIFFUSION LIMIT FOR KINETIC EQUATIONS WITH DEGENERATE COLLISION FREQUENCY
• Fractional diffusion limit for collisional kinetic equations: A moments method
• An Asymptotic-Induced Scheme for Nonstationary Transport Equations in the Diffusive Limit
• Statistical Size Distributions in Economics and Actuarial Sciences
• Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations
• Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations
• Diffusion Approximation and Computation of the Critical Size
• Micro-Macro Schemes for Kinetic Equations Including Boundary Layers
• A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit

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