Determination of the diffusivity, dispersion, skewness and kurtosis in heterogeneous porous flow. Part II: Lattice Boltzmann schemes with implicit interface

•The TRT-EMM LBM determines the first four solute distribution and RTD moments from any streamwise-periodic stationary velocity field.•The temporal and spatial moments are computed within the same run; the full dispersion tensor can be predicted from d independent computations.•The TRT-EMM is examined analytically in stratified flow and Darcy flow through porous blocks in “series”; interface analysis applies to general LBM-ADE..•Two direct transient heterogeneous LBM-ADE schemes are compared with TRT-EMM in Brinkman flow around porous obstacles.•The TRT-EMM is numerical-diffusion free; it is much faster and more capable for mesh refinement and high Péclet range than LBM-ADE.