Modeling the effects of slip on dipole–wall collision problems using a lattice Boltzmann equation method

Abstract

We study the physics of flow due to the interaction between a viscous dipole and boundaries that permit slip. This includes partial and free slip, and interactions near corners. The problem is investigated by using a two relaxation time lattice Boltzmann equation with moment-based boundary conditions. Navier-slip conditions, which involve gradients of the velocity, are formulated and applied locally. The implementation of free-slip conditions with the moment-based approach is discussed. Collision angles of 0°, 30°, and 45° are investigated. Stable simulations are shown for Reynolds numbers between 625 and 10 000 and various slip lengths. Vorticity generation on the wall is shown to be affected by slip length, angle of incidence, and Reynolds number. An increase in wall slippage causes a reduction in the number of higher-order dipoles created. This leads to a decrease in the magnitude of the enstrophy peaks and reduces the dissipation of energy. The dissipation of the energy and its relation to the enstrophy are also investigated theoretically, confirming quantitatively how the presence of slip modifies this relation.

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

“…We note that most previous applications of moment-based boundary conditions [16,29,30,[38][39][40] impose a Navier-Stokes stress condition, Γ xx = 0 at a boundary but this has been shown to be inconsistent with the underlying moment system [28,33].…”

“…and the flow velocity is given by equation (31). The computed solution with the Navier-Stokes stress condition Γ xx = 0 that has often been used with the moment-based approach [16,30,38,39,41] is also shown. The resolution is the same as above and the results are grid independent.…”

“…Alternatively, a novel technique for implementing boundary conditions in the lattice Boltzmann method was proposed by Bennett [29] and used to impose the Navier-Maxwell conditions precisely for slip flow in microchannels by Reis and Dellar [16]. This methodology does not produce any artificial slip and can be used with any lattice Boltzmann collision operator [30][31][32]. It can also be used to impose boundary conditions that are consistent with the deviatoric stress and has been shown to predict non-Navier-Stokes behaviour [28,33], but until now this has not been used to compute the slip-flow regime.…”

Mass-balance and locality versus accuracy with the new boundary and interface-conjugate approaches in advection-diffusion lattice Boltzmann method

“…Indeed, these two collision models automatically reduce to the two-relaxation-time TRT collision, 25,29 which is simpler, lattice independent, and more computationally efficient; additionally, the TRT allows for the solution parametrization, stability, and boundary/interface control with the help of the specific combination K of its two relaxation rates; moreover, the optimal TRT-ADE stability choice 31 K ¼ 1 4 remains robust in high Reynolds fluid flow modeling. 79 The methodology developed in the present work is especially compact with the TRT collision but it extends for any linear collision operator. Numerically, we solve steadystate linear ADE with the recent (stationary) S-TRT formulation 40 where (i) an arbitrary physical and model parameter range is available, because the S-TRT is quite insensitive to the transient stability restrictions and P eclet range, and (ii) the modeled solution is fixed by the grid P eclet number U=D 0 and K for any diffusion collision rate.…”