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This work presents a kinetic wall boundary model for diatomic gas molecules. The model is derived by generalizing the Cercignani-Lampis-Lord gas-surface interaction kernel in order to account for the gas internal degrees of freedom. Here, opposed to the extensions by Lord ["Some extensions to the Cercignani-Lampis gas-surface scattering kernel," Phys. Fluids 3, 706-710 (1991)], energy exchange between different molecular modes is honored and thus, different physical phenomena arising from inelastic gas-surface collisions can be described. For practical implementations of the model, a Monte-Carlo algorithm was devised, which significantly reduces the computational cost associated with sampling. Comparisons of model predictions with experimental and molecular dynamics data exhibit good agreement. Moreover, simulation studies are performed to demonstrate how energy transfers between different modes due to wall collisions can be exploited for gas separation. [ABSTRACT FROM AUTHOR]

We introduce a framework for generating samples of a distribution given a finite number of its moments, targeted at particle-based solutions of kinetic equations and rarefied gas flow simulations. Our model, referred to as the Wasserstein-Entropy distribution (WE), couples a physically-motivated Wasserstein penalty term to the traditional maximum-entropy distribution (MED) function, which serves to regularize the latter. The penalty term becomes negligible near the local equilibrium, reducing the proposed model to the MED, known to reproduce the hydrodynamic limit. However, in contrast to the standard MED, the proposed WE closure can cover the entire physically realizable moment space, including the so-called Junk line. We also propose an efficient Monte Carlo algorithm for generating samples of the unknown distribution which is expected to outperform traditional non-linear optimization approaches used to solve the MED problem. Numerical tests demonstrate that given moments up to the heat flux—that is, information equivalent to that contained in the Chapman-Enskog distribution—the proposed methodology provides a reliable closure in the collision-dominated and early transition regimes. Applications to greater rarefaction demand information from higher-order moments, which can be incorporated within the proposed closure. • Generate samples from distribution defined by small number of its moments. • Solution based on entropic optimal transport. • Resulting distribution is well defined for all realizable moments. • Samples generated using efficient Monte Carlo algorithm. • Validated using DSMC simulations of rarefied gas hydrodynamics. [ABSTRACT FROM AUTHOR]

• 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. [ABSTRACT FROM AUTHOR]