Generic boundary conditions for lattice Boltzmann models and their application to advection and anisotropic dispersion equations

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Consistent initial conditions for lattice Boltzmann simulations (2006, methodology): “The above equation is the general diffusion–advection equation for the passive scalar q [14,15].”
Study of Simple Hydrodynamic Solutions with the Two-Relaxation-Times Lattice Boltzmann Scheme (2008, methodology): “The TRT evolution equation [12, 13, 16] describes the relaxation of the populations { fq} to prescribed equilibrium functions {eq }:”
Two-Relaxation-Time Lattice Boltzmann Scheme: About Parametrization, Velocity, Pressure and Mixed Boundary Conditions (2008, methodology): “The principal difference from the boundary schemes [18] for the advection-diffusion equations is in the treatment of”
Lattice Boltzmann methods for multiphase flow and phase-change heat transfer (2015, methodology): “Furthermore, Ginzburg [228] has proposed a multi-reflection scheme to mimic the Dirichlet and Neumann boundary conditions in the LB models for advection and anisotropic dispersion equations with arbitrarily shaped surfaces.”
An evaluation of lattice Boltzmann schemes for porous medium flow simulation (2006, methodology): “One can also modify the MR relation of Eq. (14a) by, for example, replacing fR(xD, tn+1) with fR(xD, tn), as indicated in [22, 27 ].”