Analysis of a new class of forward semi-Lagrangian schemes for the 1D Vlasov Poisson equations |
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Authors: | Thomas Respaud Eric Sonnendrücker |
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Institution: | 1.IRMA,Université de Strasbourg and INRIA-Nancy-Grand Est, CALVI Project-Team,Strasbourg,France |
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Abstract: | The Vlasov equation is a kinetic model describing the evolution of a plasma which is a globally neutral gas of charged particles.
It is self-consistently coupled with Poisson’s equation, which rules the evolution of the electric field. In this paper, we
introduce a new class of forward semi-Lagrangian schemes for the Vlasov–Poisson system based on a Cauchy Kovalevsky (CK) procedure
for the numerical solution of the characteristic curves. Exact conservation properties of the first moments of the distribution
function for the schemes are derived and a convergence study is performed that applies as well for the CK scheme as for a
more classical Verlet scheme. A L
1 convergence of the schemes will be proved. Error estimates in
O(Dt2+h2 + \frach2Dt){O\left(\Delta{t}^2+h^2 + \frac{h^2}{\Delta{t}}\right)} for Verlet] are obtained, where Δt and h = max(Δx, Δv) are the discretization parameters. |
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Keywords: | |
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