2025/09/08 by Veronica Montanaro, Montanaro, Veronica, Lukas Netterdon +5
Physics and Astronomy · #60J60 #65C20 #82C40 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Numerical Analysis (math.NA) #Optical properties and cooling technologies in crystalline materials #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2509.06610
openalex publication_date 2025/09/08 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28
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.