  The lattice-Boltzmann method (LBM) and its variants have emerged as
promising, computationally efficient and increasingly popular numerical methods
for modelling complex fluid flow. However, it is acknowledged that the method
can demonstrate numerical instabilities, e.g., in the vicinity of shocks. We
propose a simple and novel technique to stabilise the lattice-Boltzmann method
by monitoring the difference between microscopic and macroscopic entropy.
Populations are returned to their equilibrium states if a threshold value is
exceeded. We coin the name Ehrenfests' steps for this procedure in homage to
the vehicle that we use to introduce the procedure, namely, the Ehrenfests'
idea of coarse-graining. The one-dimensional shock tube for a compressible
isothermal fluid is a standard benchmark test for hydrodynamic codes. We
observe that, of all the LBMs considered in the numerical experiment with the
one-dimensional shock tube, only the method which includes Ehrenfests' steps is
capable of suppressing spurious post-shock oscillations.
