Higher order mixed moment approximations for the Fokker-Planck equation   in one space dimension
  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. 
Florian Schneider, Graham Alldredge, Martin Frank, Axel Klar
math-ph math.AP math.MP