Entropic Fokker-Planck kinetic model

• Published in: Journal of computational physics Vol. 430; p. 110034
• Main Authors: Gorji, M. Hossein, Torrilhon, Manuel
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 01.04.2021; Elsevier Science Ltd
• Subjects: Boltzmann equation; Boltzmann transport equation; Collisions; Computational physics; Couette flow; Diffusion; Direct simulation Monte Carlo method; DSMC; Fokker-Planck equation; Monatomic gases; Monte-Carlo; Prandtl number; Rarefied gas flows; Rarefied gases; Shock wave profiles; Shock waves; Simulation; Stochastic processes; Theorems; Monte-Carlo; Boltzmann equation; Fokker-Planck equation; DSMC; Rarefied gas flows
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2020.110034

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