Entropic equilibrium for the lattice Boltzmann method: Hydrodynamics and numerical properties

The entropic lattice Boltzmann framework proposed the construction of the equilibrium by taking into consideration minimization of a discrete entropy functional. The effect of this entropic equilibrium on properties of the resulting solver has been the topic of discussions in the literature. Here we present a rigorous analysis of the hydrodynamics and numerics of the entropic equilibrium. We demonstrate that the entropic equilibrium features unconditional linear stability, in contrast to the conventional polynomial equilibrium. We reveal the mechanisms through which unconditional linear stability is maintained, most notable of which are adaptive propagation velocity of normal modes and the positive-definite nature of the dissipation rates of hydrodynamic eigenmodes. We further present a simple local correction to considerably reduce the deviations in the effective bulk viscosity.