Impact of Entropy in Shock Recovery Through Fokker-Planck Kinetics

Abstract While numerical methods based on the Boltzmann equation are often computationally demanding in near-continuum regime, Fokker-Planck approximations can offer efficient alternative. However, existing Fokker-Planck models remain largely heuristic and often lack global accuracy across diverse kinetic regimes, from micro-nano fluidics to the hypersonic setups. We propose a systematic recipe to construct Fokker-Planck models with special emphasis on the role of entropy and its evolution. We make the case that the Fisher entropic constraint is a key to build viable Fokker-Planck models, particularly for resolving physically accurate shock profiles. Our arguments are supported by numerical tests on a two-dimensional shock problem.