Integer Lattice Gas with a sampling collision operator for the fluctuating Navier-Stokes Equation

This paper constitutes a step in the direction of developing integer lattice gas methods as an attractive alternative to lattice Boltzmann methods. Here we show that to Boltzmann limit the one dimensional Blommel integer lattice gas is very close to entropic lattice Boltzmann. More interestingly the integer lattice gas retains additional correlations that prevent the existence of a well defined Boltzmann limit. In the analysis of the decaying sine wave we will see that in some situations the bulk viscosity can crucially depend on such correlations beyond the Boltzmann limit. A sampling collision operator, introduced here, can speed up the execution time to make the algorithm obtain comparable computational efficiency to entropic lattice Boltzmann methods.