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

Abstract: The entropic lattice Boltzmann framework proposed the construction of the discrete equilibrium by taking into consideration minimization of a discrete entropy functional. The effect of this form of the discrete 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. In doing so 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 guaranteed, most notable of which the adaptive normal modes propagation velocity and the positive-definite nature of the dissipation rates of all eigen-modes. We further present a simple local correction to considerably reduce the deviations in the effective bulk viscosity.