Lattice Boltzmann method with moment-based boundary conditions for rarefied flow in the slip regime

Abstract

A lattice Boltzmann method with moment-based boundary conditions is used to compute flow in the slip regime. Navier-Maxwell slip conditions and Burnett-order stress conditions that are consistent with the discrete velocity Boltzmann equation are imposed locally on stationary and moving boundaries. Micro Couette and micro lid driven driven cavity flows are studied numerically at Knudsen and Mach numbers of the order O(10 −1 ). The Couette results for velocity and the deviatoric stress at second order in Knudsen number are in excellent agreement with analytical solutions and the cavity results are in excellent agreement with existing data. The algorithm is shown to compute nonequilibrium effects in the pressure that are in very good agreement with DSMC simulations of the Boltzmann equation but not captured by the Navier-Stokes equations.

Exponential distribution functions for positivity-preserving lattice Boltzmann schemes: Application to 2D compressible flow simulations

“…As future works, we will show how to derive positivity-preserving initial and boundary conditions, for static and adaptive lattices, by directly imposing these conditions in the moment space, in a similar manner to what is done for standard LBMs. [125][126][127][128][129] Nonreflecting boundary conditions 130 will also be investigated to get closer to the requirements of computational aeroacoustics simulations of industrial applications. Interestingly, relying on exponential distributions only implies local changes of the standard collide-and-stream algorithm.…”

Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

“…To the best of the authors' knowledge, those MR slip schemes 21,22 are the only existing pathway in LBM to reproduce Equation ( 1) within a parabolic level of accuracy, for any arbitrary shaped walls. Alternative LBM slip strategies either support the parabolic accuracy limited to lattice-aligned surfaces 34,[36][37][38][39] or, otherwise, exhibit a degraded accuracy (lowering from second-to first-order) when applied to nonmesh aligned walls. [40][41][42][43][44] Still, despite the superior accuracy of the MR-based slip boundary schemes, 21,22 they carry a few points worthwhile improvement, namely: (i) nonlocality of implementation, for example, requiring at least two nodes to accommodate arbitrarily rotated parabolic solutions; (ii) inadequacy of the scheme to operate on edge/corner nodes due to the lack of neighboring nodes; and (iii) inherent difficulty to independently prescribe normal/tangential conditions in a linkwise manner.…”

“…As application domain, we focus on the simulation of microchannel slip flows. While in the LBM context this benchmark has been largely studied for 2D channel geometries, 21,[36][37][38][39][40][41]44 its extension to 3D ducts has received considerable less attention, apart from a few exceptions that modeled the slip condition on circular tubes 43 and rectangular ducts. 43,49 Unlike for no-slip walls, the assessment of convergence rates and other accuracy measures have been scarcely reported for slip-flow problems, particularly when the wall does not align with the LBM uniform Cartesian mesh, 21,41,42 much seldom in 3D domains.…”

Influence of surface properties on the dynamics of fluid flow

“…27 Various other papers present how gas-surface scattering models form the basis for determining boundary conditions used to solve either the Boltzmann equation (kinetic theory) or Navier-Stokes equations (continuum-based approach), such as papers authored by Brull, 28 Coron, 29 Shen, Chen et al, 30 Hattori et al, 31 Aoki et al, 32 Kosuge et al, 33 and Duan. 34 Other papers analyzed flow of gases near solid surfaces using both analytical and numerical methods (lattice Boltzmann method or molecular dynamics) in the scope of kinetic theory, such as Ben-Ami and Manela, 35 while other authors considered numerical approaches only, such as Silva et al, 36,37 Mohammed and Reis, 38 Shan, 39 Ou and Chen, 40 Liang et al, 41 and Varghese et al 42 Most of these previously mentioned deliberations assumed simple atom-surface scattering models, such as the diffuse-specular scattering kernel, which does not account for any spatial variations of scattering properties, and focused on solving the Boltzmann equation and determining statistical averages in an entire domain of fluid adjacent to the surface in question.…”