Second-order mixed-moment model with differentiable ansatz function in slab geometry

TL;DR

This paper introduces a differentiable mixed-moment model for the Fokker-Planck equation in one dimension, improving upon existing models by addressing the zero net-flux problem and demonstrating its effectiveness through numerical tests.

Contribution

The paper develops a second-order mixed-moment model with a differentiable ansatz function, providing new realizability theory and numerical validation in slab geometry.

Findings

Overcomes zero net-flux issue of classical models

Shows improved accuracy over $M_N$ and $P_N$ schemes

Validates the model with numerical experiments

Abstract

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.