A consistent hydrodynamic boundary condition for the lattice Boltzmann method

Abstract

A hydrodynamic boundary condition is developed to replace the heuristic bounce-back boundary condition used in the majority of lattice Boltzmann simulations. This boundary condition is applied to the two-dimensional, steady flow of an incompressible fluid between two parallel plates. Poiseuille flow with stationary plates, and a constant pressure gradient is simulated to machine accuracy over the full range of relaxation times and pressure gradients. A second problem involves a moving upper plate and the injection of fluid normal to the plates. The bounce-back boundary condition is shown to be an inferior approach for simulating stationary walls, because it actually mimics boundaries that move with a speed that depends on the relaxation time. When using accurate hydrodynamic boundary conditions, the lattice Boltzmann method is shown to exhibit second-order accuracy.

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

“…2 shows the incoming distribution functions as dashed lines and the full lines represent the known functions. Bennett [16] argued that, similar in spirit to Noble et al [17], we can calculate the unknown distribution functions purely from constraints imposed on the hydrodynamic moments at the boundary. The basic idea of this method is summarised as follows.…”

“…The presented boundary conditions, the so-called "Moment Method", are another way to impose conditions directly upon the moments of the LBM [16]. The momentbased implementation discussed here uses only hydrodynamic moments to satisfy boundary conditions and may be viewed as a direct extension of the method first proposed by Noble et al [17] for simpler lattices. The moment method has already been applied to diffusive slip [18], natural convection problems [19], the slipflow regime [20], and wetting phenomena in multiphase flow [21], and reported very favourable results.…”

An Accurate Curved Boundary Treatment in the Lattice Boltzmann Method

“…It has been shown that the BBL scheme gives second-order accurate result for straight walls [33,19]. Noble et al developed a second-order accurate boundary condition to compute f s but it is only applicable to straight walls in triangular lattice space [27]. He et al generalized the scheme of Noble et al to arbitrary lattice [19].…”

Lattice-Boltzmann and finite-difference simulations for the permeability for three-dimensional porous media

“…Some of these more sophisticated solid-fluid boundaries are restricted to regular geometries [28,29], but there are also general boundary-fitted models [30,31] available. For practical simulations the bounce-back boundary is however very attractive, because it is a simple and computationally efficient method for imposing no-flow conditions on irregularly shaped walls.…”