Mirror states enable lower viscosity lattice gases

Abstract

We developed a method for significantly lowering the viscosity achievable for a hydrodynamic lattice gas method. The key advance is the derivation of a mirror state that allows for a reduction of viscosity by more than an order of magnitude over existing lattice gas methods.

Figures (3)

• Figure 1: An illustration of the flipping operation for $N=9$, $J=0$, and an initial $\pi$ value of $2$. The forward ($\pi$) and backward ($\pi^m$) cumulative distributions are given by
• Figure 2: Extracted maxima of decaying sound waves with initial average densities of $\bar{N}^{eq}$=100, 1,000, and 10,000 and a system size of 100 lattice sites, shown on a logarithmic scale. All systems were initialized identically to those in our prior paper, and run for 30,000 timesteps with an $\omega_\mathrm{eff}$ value of 1.5, and then averaged over 2,500,000/$\bar{N}^{eq}$ random seeds. The theoretical decay rate of a BGK system calculated using Eqs. (\ref{['eqn: BGKVisc']}) and (\ref{['eqn: nuAndlambda']}) is also shown, along with late time fittings (LT) for each density generated via xmgrace non-linear curve fitting. See text for additional details about the late time fittings.
• Figure 3: The viscosity recovered for early time (ET - $t<500$) and late time (LT - found via the method used in Fig. \ref{['fig: DecayRate']}) systems, shown on a logarithmic scale. These systems were initialized and run identically to those in Fig. \ref{['fig: DecayRate']} for $\omega_\mathrm{eff}$ ranging from 0.1 to 2. The error in these viscosities, calculated by simulating the same system using multiple sets of random seeds, is on the order of the symbol size. Eq. (\ref{['eqn: BGKVisc']}) is also shown.