Entropic lattice Boltzmann methods: A review

Abstract

In the late 90's and early 2000's the concept of a discrete H theorem and Lyapunov functionals as a way to ensure stability of lattice Boltzmann solvers was a shift of paradigm in the construction of discrete kinetic solvers and opened the door for new discussions and perspectives on the matter. The entropic construction proposed to reorganize the relaxation collision operator by changing both the equilibrium attractor and relaxation process by introducing a discrete entropy functional and enforcing an H-theorem. The concept has proven to be effective in stabilizing lattice Boltzmann solvers in a variety of different area of applications ranging from isothermal weakly compressible, to fully compressible and multi-phase flows. Here we review basic building blocks of the entropic lattice Boltzmann method and discuss its extension to multiphase and compressible flows.