Entropic lattice Boltzmann methods

We present a general methodology for constructing lattice Boltzmann models of hydrodynamics with certain desired features of statistical physics and k inetic theory. We show how a methodology of linear programming theory, know n as Fourier-Motzkin elimination, provides an important tool for visualizin g the state-space of lattice Boltzmann algorithms that conserve a given set of moments of the distribution function. We show how such models can be en dowed with a Lyapunov functional, analogous to Boltzmann's H, resulting in unconditional numerical stability. Using the Chapman-Enskog analysis and nu merical simulation, we demonstrate that such entropically stabilized lattic e Boltzmann algorithms, while fully explicit and perfectly conservative, ma y achieve remarkably low values for transport coefficients, such as viscosi ty. Indeed, the lowest such attainable values are limited only by considera tions of accuracy, rather than stability. The method thus holds promise for high-Reynolds-number simulations of the Navier-Stokes equations.