Analytical calculation of slip flow in lattice Boltzmann models with kinetic boundary conditions

We present a mathematical formulation of kinetic boundary conditions for Lattice Boltzmann schemes in terms of reflection, slip, and accommodation coefficients. It is analytically and numerically shown that, in the presence of a non-zero slip coefficient, the Lattice Boltzmann flow develops a physical slip flow component at the wall. Moreover, it is shown that the slip coefficient can be tuned in such a way to recover quantitative agreement with analytical and experimental results up to second order in the Knudsen number.Comment: 27 pages, 4 figure

Variational approach to gas flows in microchannels on the basis of the Boltzmann equation for hard-sphere molecules

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.The objective of the present paper is to provide an analytic expression for the first- and second-order velocity slip coefficients. Therefore, gas flow rates in microchannels have been rigorously evaluated in the near-continuum limit by means of a variational technique which applies to the integrodifferential form of the Boltzmann equation based on the true linearized collision operator. The diffuse-specular reflection condition of Maxwell’s type has been considered in order to take into account the influence of the accommodation coefficient on the slip parameters. The polynomial form of Knudsen number obtained for the Poiseuille mass flow rate and the values of the second order velocity slip coefficients found on the basis of our variational solution of the linearized Boltzmann equation for hardsphere molecules are analyzed in the frame of potential applications of classical continuum numerical tools (as lattice Boltzmann methods) in simulations of microscale flows

A revisit to the Cercignani–Lampis model: Langevin picture and its numerical simulation

Part of the Springer INdAM Series book series (SINDAMS, volume 48)The Workshop INdAM "Recent advances in kinetic equations and applications", which took place in Rome (Italy), from November 11th to November 15th, 2019.The Cercignani–Lampis (CL) model for the gas–surface interaction is revisited from the Langevin dynamics viewpoint. Starting from a time-independent Fokker–Planck formalism by Cercignani, its time-dependent extension and the corresponding Langevin description are introduced. The Langevin description sheds light on dynamical features of a stochastic process corresponding to the CL model. Numerical simulations on the basis of the Langevin description are performed as well to reproduce the scattering kernel and reflection intensity distribution numerically. Although the noise in the stochastic process is apparently simple, the Milstein scheme rather than the Euler–Maruyama scheme has to be adopted to achieve a satisfactory numerical convergence in time discretisation

Assessment of Gas-Surface Interaction Models for Computation of Rarefied Hypersonic Flow

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76727/1/AIAA-36375-113.pd

Slip and Jump Coefficients for General Gas-Surface Interactions According to the Moment Method

We develop a moment method based on the Hermite series of arbitrary order to calculate viscous-slip, thermal-slip, and temperature-jump coefficients for general gas-surface scattering kernels. Under some usual assumptions of scattering kernels, the solvability is obtained by showing the positive definiteness of the symmetric coefficient matrix in the boundary conditions. For gas flows with the Cercignani-Lampis gas-surface interaction and inverse-power-law intermolecular potentials, the model can capture the slip and jump coefficients accurately with elegant analytic expressions. On the one hand, the proposed method can apply to the cases of arbitrary order moments with increasing accuracy. On the other hand, the explicit formulae for low-order situations are simpler and more accurate than some existing results in references. Therefore, one may apply these formulae in slip and jump conditions to improve the accuracy of macroscopic fluid dynamic models for gas flows

Comparisons of the Maxwell and CLL Gas/Surface Interaction Models Using DSMC

Two contrasting models of gas-surface interactions are studied using the Direct Simulation Monte Carlo (DSMC) method. The DSMC calculations examine differences in predictions of aerodynamic forces and heat transfer between the Maxwell and Cercignani-Lampis-Lord (CLL) models for flat plate configurations at freestream conditions corresponding to a 140 km orbit around Venus. The size of the flat plate is that of one of the solar panels on the Magellan spacecraft, and the freestream conditions are one of those experienced during aerobraking maneuvers. Results are presented for both a single flat plate and a two-plate configuration as a function of angle of attack and gas-surface accommodation coefficients. The two plate system is not representative of the Magellan geometry, but is studied to explore possible experiments that might be used to differentiate between the two gas surface interaction models