Equilibrium Distribution Functions in Entropic Lattice Boltzmann Method

The lattice Boltzmann method is a numerical scheme for mesoscopic description between the molecular level and the micelle level. Instabilities of lattice Boltzmann method for turbulence simulation were improved by the entropic lattice Boltzmann method. However, the theoretical research of entropic lattice Boltzmann method is not yet mature, and theories of equilibrium distribution functions are divided into two schools. Aimed at high Reynolds number turbulence simulation based on the entropic lattice Boltzmann method, the entropy form, the third-order polynomial form and second-order polynomial form of equilibrium distribution functions were compared. Concerned variables contained the vertical velocity, strain rate tensor and component of equilibrium distribution functions. Conclusion: as for entropic lattice Boltzmann method for turbulence simulations, polynomial forms of equilibrium distribution function perform a significantly higher efficiency than the entropy form while the entropy form of equilibrium distribution function can achieve a higher stability.