An Asymptotic-Preserving Scheme for the Kinetic Equation with Anisotropic Scattering: Heavy Tail Equilibrium and Degenerate Collision Frequency

2019 ◽  
Vol 41 (1) ◽  
pp. A422-A451
Author(s):  
Li Wang ◽  
Bokai Yan
Keyword(s):  
Kinetic Equation ◽  
Collision Frequency ◽  
Anisotropic Scattering ◽  
Heavy Tail ◽  
Asymptotic Preserving ◽  
Asymptotic Preserving Scheme

scholarly journals An Asymptotic Preserving Scheme for Kinetic Models for Chemotaxis Phenomena

2018 ◽  
Vol 9 (2) ◽  
pp. 61-75
Author(s):  
Abdelghani Bellouquid ◽  
Jacques Tagoudjeu
Keyword(s):  
Kinetic Equation ◽  
Kinetic Model ◽  
Small Parameter ◽  
Kinetic Models ◽  
Numerical Approach ◽  
Test Cases ◽  
Equivalent Formulation ◽  
Asymptotic Preserving ◽  
Standard Methods ◽  
Asymptotic Preserving Scheme

Abstract In this paper, we propose a numerical approach to solve a kinetic model of chemotaxis phenomena. This scheme is shown to be uniformly stable with respect to the small parameter, consistent with the uid-di usion limit (Keller-Segel model). Our approach is based on the micro-macro decomposition which leads to an equivalent formulation of the kinetic model that couples a kinetic equation with macroscopic ones. This method is validated by various test cases and compared to other standard methods.

scholarly journals Hybrid model for the Coupling of an Asymptotic Preserving scheme with the Asymptotic Limit model: The One Dimensional Case

2011 ◽  
Vol 32 ◽  
pp. 23-30 ◽  
Author(s):  
Pierre Degond ◽  
Fabrice Deluzet ◽  
Dario Maldarella ◽  
Jacek Narski ◽  
Claudia Negulescu ◽  
...  
Keyword(s):  
Hybrid Model ◽  
Asymptotic Limit ◽  
Dimensional Case ◽  
Asymptotic Preserving ◽  
One Dimensional ◽  
Limit Model ◽  
Asymptotic Preserving Scheme ◽  
The One
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