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arXiv · 1405.5305

Higher order mixed moment approximations for the Fokker-Planck equation in one space dimension

Florian Schneider·Graham Alldredge·Martin Frank·Axel Klar
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Abstract

We study mixed-moment models (full zeroth moment, half higher moments) for a Fokker-Planck equation in one space dimension. Mixed-moment minimum-entropy models are known to overcome the zero net-flux problem of full-moment minimum entropy Mn models. Realizability theory for these mixed moments of arbitrary order is derived, as well as a new closure, which we refer to as Kershaw closures. They provide non-negative distribution functions combined with an analytical closure. Numerical tests are performed with standard first-order finite volume schemes and compared with a finite-difference Fokker-Planck scheme.

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Florian Schneider, Graham Alldredge, Martin Frank, Axel Klar. 2014-05-21. Higher order mixed moment approximations for the Fokker-Planck equation in one space dimension. https://arxiv.org/abs/1405.5305

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