  The study of the underlying physics of soft flowing materials depends heavily
on numerical simulations, due to the complex structure of the governing
equations reflecting the competition of concurrent mechanisms acting at widely
disparate scales in space and time. A full-scale computational modelling
remains a formidable challenge since it amounts to simultaneously handle six or
more spatial decades in space and twice as many in time. Coarse-grained methods
often provide a viable strategy to significantly mitigate this issue, through
the implementation of mesoscale supramolecular forces designed to capture the
essential physics at a fraction of the computational cost of a full-detail
description.
  Here, we review some recent advances in the design of a lattice Boltzmann
mesoscale approach for soft flowing materials, inclusive of near-contact
interactions (NCI) between dynamic interfaces, as they occur in high
packing-fraction soft flowing crystals.
  The method proves capable of capturing several aspects of the rheology of
soft flowing crystals, namely, i) a 3/2 power-law dependence of the dispersed
phase flow rate on the applied pressure gradient, ii) the structural transition
between an ex-two and ex-one (bamboo) configurations with the associated drop
of the flow rate, iii) the onset of interfacial waves once NCI is sufficiently
intense.
