  We construct a system of nonequilibrium entropy limiters for the lattice
Boltzmann methods (LBM). These limiters erase spurious oscillations without
blurring of shocks, and do not affect smooth solutions. In general, they do the
same work for LBM as flux limiters do for finite differences, finite volumes
and finite elements methods, but for LBM the main idea behind the construction
of nonequilibrium entropy limiter schemes is to transform a field of a scalar
quantity - nonequilibrium entropy. There are two families of limiters: (i)
based on restriction of nonequilibrium entropy (entropy "trimming") and (ii)
based on filtering of nonequilibrium entropy (entropy filtering). The physical
properties of LBM provide some additional benefits: the control of entropy
production and accurate estimate of introduced artificial dissipation are
possible. The constructed limiters are tested on classical numerical examples:
1D athermal shock tubes with an initial density ratio 1:2 and the 2D lid-driven
cavity for Reynolds numbers Re between 2000 and 7500 on a coarse 100*100 grid.
All limiter constructions are applicable for both entropic and non-entropic
quasiequilibria.
