Using the Lid-Driven Cavity Flow to Validate Moment-Based Boundary Conditions for the Lattice Boltzmann Equation

Abstract

The accuracy of the Moment Method for imposing no-slip boundary conditions in the lattice Boltzmann algorithm is investigated numerically using lid-driven cavity flow. Boundary conditions are imposed directly upon the hydrodynamic moments of the lattice Boltzmann equations, rather than the distribution functions, to ensure the constraints are satisfied precisely at grid points. Both single and multiple relaxation time models are applied. The results are in excellent agreement with data obtained from state-of-the-art numerical methods and are shown to converge with second order accuracy in grid spacing.

Assessing moment-based boundary conditions for the lattice Boltzmann equation: A study of dipole-wall collisions

“…The moment-based method is similar in spirit to Noble et al's approach but is far more general in terms of the types of boundary conditions that can be implemented and the lattice stencils they can be applied too. Moment based boundary conditions have been applied to several flows and problems already [46,21,46,44,47,48]. However, a detailed study of moment-based boundary conditions for no-slip flows has not been conducted.…”

Moment‐based boundary conditions for straight on‐grid boundaries in three‐dimensional lattice Boltzmann simulations

“…In addition, no stable SRT results were obtained at Re=1000. For comparison, the grid convergence results of the 2D moment‐based boundary conditions obtained by Mohammed and Reis 43 using MRT and Reis 38 using TRT have been included. The results of Mohammed and Reis show better accuracy at Re=100, but interestingly the results of the present 3D TRT‐LBM moment‐based boundary conditions at Re=1000 show slightly improved overall accuracy in comparison to the 2D lattice models.…”

“…Velocity field (left) and streamlines (middle) at Re=1000. Grid convergence (right) of the two‐dimensional lid‐driven cavity flow case using the moment‐based boundary conditions, and comparison with the results of Reis 38 and Mohammed and Reis 43 The relaxation time τ + is defined via Re and τ − is chosen so that Λ=1/4 [Colour figure can be viewed at wileyonlinelibrary.com]…”

“…For some cases, even when using the more sophisticated TRT collision scheme, it has been observed that the more ‘physical’ or the asymmetric choice of moments on the corner boundary can lead to instabilities and further to the solution divergence at higher Reynolds numbers. However, the problem can be resolved by choosing a symmetric set of velocity moments, as predicted by Mohammed and Reis 43 . Unfortunately, sometimes it means dropping the condition for the hydrodynamic moment in favor of the third‐order moment, such as at edges and corners.…”

“…The LBM with moment‐based boundary conditions has been successfully applied to various physical systems, where exact hydrodynamic boundary conditions must be employed 39-42 . Furthermore, its stability and accuracy has also been commented on briefly, 43 and some theoretical analysis has been performed, 37 but there is still room for an in‐depth stability analysis. Studying stability of the present 3D method is left for future research.…”