Entropic Fokker-Planck kinetic model

The diffusion limit of kinetic systems has been subject numerous studies since prominent works Lebowitz et al. [1] and van Kampen [2]. More recently, the topic seen a fresh interest from rarefied gas simulation perspective. In particular, Fokker-Planck based models provide novel approximations Boltzmann equation, where relaxation induced by binary collisions is modeled via continuous stochastic processes. Hence in contrast to direct Monte-Carlo, computational particles follow seemingly independent paths. As result, significant gain at small/vanishing Knudsen numbers can be obtained, dynamics overwhelmed collisions. cubic equation derived [3] gives rise correct viscosity Prandtl number for monatomic gases hydrodynamic limit, further accurate behavior moderate numbers. Yet model lacks rigorous structure more crucially does not admit H-theorem. latter underpins its accuracy e.g. predicting shock wave profiles. This study addresses bridging gap between processes introducing Entropic-Fokker-Planck model. drift-diffusion closures model, allow an H-theorem besides honoring consistent moments. devised validated with respect Monte-Carlo high-Mach as well Couette flows. Good performance together easy compute coefficients, makes framework attractive investigation beyond equilibrium.