scholarly journals Convergence analysis of asymptotic preserving schemes for strongly magnetized plasmas

2021 ◽  
Author(s):  
Francis Filbet ◽  
L. Miguel Rodrigues ◽  
Hamed Zakerzadeh
Keyword(s):  
Convergence Analysis ◽  
Magnetized Plasmas ◽  
Asymptotic Preserving ◽  
Asymptotic Preserving Schemes

scholarly journals TWO-SCALE MACRO–MICRO DECOMPOSITION OF THE VLASOV EQUATION WITH A STRONG MAGNETIC FIELD

2013 ◽  
Vol 23 (08) ◽  
pp. 1527-1559 ◽  
Author(s):  
NICOLAS CROUSEILLES ◽  
EMMANUEL FRÉNOD ◽  
SEVER A. HIRSTOAGA ◽  
ALEXANDRE MOUTON
Keyword(s):  
Magnetic Field ◽  
Strong Magnetic Field ◽  
Vlasov Equation ◽  
Asymptotic Preserving ◽  
Asymptotic Preserving Schemes ◽  
Starting Point ◽  
Oscillating Functions ◽  
Scale Limit

In this paper, we build a two-scale macro–micro decomposition of the Vlasov equation with a strong magnetic field. This consists in writing the solution of this equation as a sum of two oscillating functions with circumscribed oscillations. The first of these functions has a shape which is close to the shape of the two-scale limit of the solution and the second one is a correction built to offset this imposed shape. The aim of such a decomposition is to be the starting point for the construction of two-scale 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>

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