An improved gray lattice Boltzmann model for simulating fluid flow in multi-scale porous media

Topology optimization of unsteady flow problems using the lattice Boltzmann method

“…Partial bounceback models were first suggested by Dardis and McCloskey [34,35]; they are probabilistic meso-scale models in which a bounceback like term dependent on the permeability of the lattice node is added to the collision step. In this work, the partial bounceback model presented by Zhu and Ma [13] is adopted. The modified collision step has the form…”

“…Discretization of this equation yields an explicit time marching scheme which can compute approximate solutions to the incompressible NS equations for low Mach number flows. The method is attractive because it is algorithmically simple, lends itself well to parallel implementation, and is relatively easy to extend to more complicated physics, such as porous media [11][12][13], or multiphase flows [14,15]. The use of the LBM for topology optimization was pioneered by Pingen et al [16], who used the density approach to topology optimization.…”

Combining effective media and multi-phase methods of Lattice Boltzmann modelling for the characterisation of liquid-vapour dynamics in multi-length scale heterogeneous structural materials

“…1 Zhu and Ma, [18], take pains to point out that σ is a model parameter but is not, in this particular implementation, strictly a solids fraction since the density function propagated, f eq , and bounced back, f , are different. They offer an improved, but computationally more complex, model where this is not the case: the same function is propagated and bounced back.…”

Gray free-energy multiphase lattice Boltzmann model with effective transport and wetting properties

“…Hitherto, these methods are limited to a single phase fluid. There are two main classes of lattice Boltzmann solvers that incorporate effective media: force-adjusted and partial bounce back methods [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. We chose to follow the partial bounce back method of Walsh et al [26] that combines computational simplicity with an ability to accurately link the partial bounce back fraction to the permeability.…”

“…The first lattice models incorporating effective media properties were developed as early as the 1990s [16][17][18][19][20][21] but they started gaining traction only recently [22][23][24][25][26][27][28][29][30]. In these models, in addition to lattice nodes assigned to be either fluid space or solid, some nodes are assigned effective media properties.…”