  We conduct an investigation into the dispersive post-shock oscillations in
the entropic lattice-Boltzmann method (ELBM). To this end we use a root finding
algorithm to implement the ELBM which displays fast cubic convergence and
guaranties the proper sign of dissipation. The resulting simulation on the
one-dimensional shock tube shows no benefit in terms of regularization from
using the ELBM over the standard LBGK method. We also conduct an experiment
investigating of the LBGK method using median filtering at a single point per
time step. Here we observe that significant regularization can be achieved.
