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arXiv · 2509.06610

Fisher entropic Fokker-Planck model of monatomic rarefied gases

Veronica Montanaro·Lukas Netterdon·Manuel Torrilhon·Hossein Gorji
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Abstract

Particle-based stochastic approximations of the Boltzmann equation are popular tools for simulations of non-equilibrium gas flows, for which the Navier-Stokes-Fourier equations fail to provide accurate description. However, these numerical methods are computationally demanding, especially in the near-continuum regime, where the collisions become overwhelming. On the other hand, the Fokker-Planck kinetic models offer an efficient alternative, as the binary collisions are described by a diffusive process. Despite the intuitive advantage, rigorous and efficient Fokker-Planck approximations of the Boltzmann equation remain an open problem. On one hand, the moment projection of the Fokker-Planck operator should be consistent with that of the Boltzmann operator. On the other hand, the Fokker-Planck model should be constructed in such a way that the H-theorem is satisfied. The central aim of this study is fulfilling these two categorically different constraints, i.e. moment matching and entropy dissipation, within a flexible and tractable Fokker-Planck framework. To this end, we introduce a Fisher information-based entropic constraint and demonstrate that, with a suitable polynomial expansion of the drift term, it is possible to simultaneously achieve weak moment matching while honouring the H-theorem. We support our theoretical result by numerical experiments on the shock problem, validating our Fisher Entropic Fokker-Planck framework.

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Veronica Montanaro, Lukas Netterdon, Manuel Torrilhon, Hossein Gorji. 2025-09-08. Fisher entropic Fokker-Planck model of monatomic rarefied gases. https://arxiv.org/abs/2509.06610

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