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Journal Articles Mathematical Models and Methods in Applied Sciences Year : 2013

Two-Scale Macro-Micro decomposition of the Vlasov equation with a strong magnetic field

Abstract

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 circonscribed 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.
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Dates and versions

hal-00638617 , version 1 (06-11-2011)
hal-00638617 , version 2 (08-11-2011)
hal-00638617 , version 3 (05-11-2012)

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Nicolas Crouseilles, Emmanuel Frenod, Sever Adrian Hirstoaga, Alexandre Mouton. Two-Scale Macro-Micro decomposition of the Vlasov equation with a strong magnetic field. Mathematical Models and Methods in Applied Sciences, 2013, 23 (08), pp.1527--1559. ⟨10.1142/S0218202513500152⟩. ⟨hal-00638617v3⟩
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