Asymptotic-Preserving Schemes for Multiscale Hyperbolic and Kinetic Equations

2017 ◽  
pp. 103-129 ◽  
Author(s):  
J. Hu ◽  
S. Jin ◽  
Q. Li
Keyword(s):  
Kinetic Equations ◽  
Asymptotic Preserving ◽  
Asymptotic Preserving Schemes

scholarly journals A criterion for asymptotic preserving schemes of kinetic equations to be uniformly stationary preserving

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Casimir Emako ◽  
Farah Kanbar ◽  
Christian Klingenberg ◽  
Min Tang
Keyword(s):  
Distribution Function ◽  
Kinetic Models ◽  
Kinetic Equations ◽  
Asymptotic Preserving ◽  
Asymptotic Preserving Schemes

<p style='text-indent:20px;'>In this work we are interested in the stationary preserving property of asymptotic preserving (AP) schemes for kinetic models. We introduce a criterion for AP schemes for kinetic equations to be uniformly stationary preserving (SP). Our key observation is that as long as the Maxwellian of the distribution function can be updated explicitly, such AP schemes are also SP. To illustrate our observation, three different AP schemes for three different kinetic models are considered. Their SP property is proved analytically and tested numerically, which confirms our observations.</p>

scholarly journals Numerical methods for kinetic equations

Acta Numerica ◽  
2014 ◽  
Vol 23 ◽  
pp. 369-520 ◽  
Author(s):  
G. Dimarco ◽  
L. Pareschi
Keyword(s):  
Computational Complexity ◽  
Numerical Methods ◽  
State Of The Art ◽  
Kinetic Equations ◽  
Numerical Techniques ◽  
Asymptotic Preserving ◽  
Hybrid Schemes ◽  
Velocity Models ◽  
Current State ◽  
Number Of Particles

In this survey we consider the development and mathematical analysis of numerical methods for kinetic partial differential equations. Kinetic equations represent a way of describing the time evolution of a system consisting of a large number of particles. Due to the high number of dimensions and their intrinsic physical properties, the construction of numerical methods represents a challenge and requires a careful balance between accuracy and computational complexity. Here we review the basic numerical techniques for dealing with such equations, including the case of semi-Lagrangian methods, discrete-velocity models and spectral methods. In addition we give an overview of the current state of the art of numerical methods for kinetic equations. This covers the derivation of fast algorithms, the notion of asymptotic-preserving methods and the construction of hybrid schemes.

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