To cite this version:Meng Liao, Quy-Dong To, Céline Léonard, Vincent Monchiet. Non-parametric wall model and methods of identifying boundary conditions for moments in gas flow equations. Physics of Fluids, American Institute of Physics, 2018, 30, pp.032008. 10
AbstractIn this paper, we use Molecular Dynamics (MD) simulation method to study gas-wall boundary conditions. Discrete scattering information of gas molecules at the wall surface are obtained from collision simulations. The collision data can be used to identify the accommodation coefficients for parametric wall models such as Maxwell, Cercignani-Lampis scattering kernels. Since these scattering kernels are based on a limited number of accommodation coefficients, we adopt nonparametric statistical methods to construct the kernel to overcome these issues. Different from parametric kernels, the non-parametric kernels require no parameter (i.e accommodation coefficients) and no predefined distribution. We also propose approaches to derive directly the Navier friction and Kapitza thermal resistance coefficients as well as other interface coefficients associated to moment equations from the non-parametric kernels. The methods are applied successfully to systems composed of CH 4 or CO 2 and graphite, which are of interest to the petroleum industry.
Global potentials for the extremely weak interaction between the He atom and gold surfaces are determined from ab initio calculations and validated with experimental-based determinations of well depth values. Dispersionless density functional periodic calculations are combined with effective pairwise functional parameters for the dispersion. These parameters are obtained from time-dependent density functional theory response theory using localized Hartree−Fock orbitals, as applied on He−Au n clusters. This He−Au pairwise potential is used in molecular dynamics simulations of gas−gold surface collisions from which incident and reflected gas atom velocities allow the determination of energy and momentum accommodation coefficients. Boundary quantities such as slip velocity and thermal resistance are not only derived from these coefficients, but also from a new methodology based on a nonparametric kernel, avoiding the atomic description of the gold surface. Similar collision simulations are performed for Ar for comparison. A model of a rough gold surface is also investigated.
In this paper, we present the construction of statistical models of gas-wall collision based on data issued from Molecular Dynamics (MD) simulations and use them to predict the velocity slip and temperature jump coefficients at the gas-solid interface. The Gaussian Mixture (GM) model, an unsupervised learning technique, is chosen for this purpose. The model shares some similarities with the well-known Cercignani-Lampis model in kinetic theory but it is more robust due to the unlimited number of Gaussian functions used and the ability to deal with correlated data of high dimensions. Applications to real gas-wall systems (Argon-Gold and Helium-Gold) confirm the good performance of the model. The trained GM model predicts physical and statistical properties including accommodation, friction and thermal conductance coefficients in excellent agreement with the MD model.
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