Second-order mixed-moment model with differentiable ansatz function in slab geometry
This work provides a theoretical and numerical foundation for mixed-moment models in kinetic theory, which is incremental for researchers working on moment methods for radiative transfer or neutron transport.
The paper develops a second-order mixed-moment model for the Fokker-Planck equation in slab geometry, addressing the zero net-flux problem of full-moment models. Numerical tests show improved accuracy over M_N and classical MM_N models, with results comparable to P_N reference schemes.
We study differentiable mixed-moment models (full zeroth and first 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 $M_N$ models. Realizability theory for these modification of mixed moments is derived for second order. Numerical tests are performed with a kinetic first-order finite volume scheme and compared with $M_N$, classical $MM_N$ and a $P_N$ reference scheme.