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Mixed-moment models, introduced before for one space dimension, are amodification of the method of moments applied to a (linear) kinetic equation,by choosing mixtures of different partial moments. They are well-suited tohandle such equations where collisions of particles are modelled with aLaplace-Beltrami operator. We generalize the concept of mixed moments to twodimension. The resulting hyperbolic system of equations has desirableproperties, removing some drawbacks of the well-known $\MN[1]$ model. Wefurthermore provide a realizability theory for a first-order system of mixedmoments by linking it to the corresponding quarter-moment theory. Additionally,we derive a type of Kershaw closures for mixed- and quarter-moment models,giving an efficient closure (compared to minimum-entropy models). The derivedclosures are investigated for different benchmark problems.

First-order quarter- and mixed-moment realizability theory and Kershaw closures for a Fokker-Planck equation in two space dimensions