Relaxation-rate formula for the entropic lattice Boltzmann model

Single relaxation time model for entropic lattice Boltzmann methods.

For lattice Boltzmann methods based on entropy functions, we derive a collision integral which enables simple identification of transport coefficients, and which circumvents construction of the equilibrium. Implementation of the two-dimensional hydrodynamics demonstrates considerable increase of stability with respect to conventional lattice Boltzmann schemes.

Entropic Lattice Boltzmann Methods

We present a general methodology for constructing lattice Boltzmann models of hydrodynamics with certain desired features of statistical physics and kinetic theory. We show how a methodology of linear programming theory, known as Fourier-Motzkin elimination, provides an important tool for visualizing the state space of lattice Boltzmann algorithms that conserve a given set of moments of the dis...

Entropic lattice Boltzmann method for microflows

A new method for the computation of flows at the micrometer scale is presented. It is based on the recently introduced minimal entropic kinetic models. Both the thermal and isothermal families of minimal models are presented, and the simplest isothermal entropic lattice Bhatnagar-Gross-Krook (ELBGK) is studied in detail in order to quantify its relevance for microflow simulations. ELBGK is equi...

Entropic and multiple relaxation time lattice Boltzmann methods compared for time harmonic flows

Variational formula for the relaxation time in the Boltzmann equation.

The relaxation time approximation (RTA) is commonly employed in nonequilibrium statistical mechanics to approximate solutions to the Boltzmann equation in terms of an exponential relaxation to equilibrium. Despite its common use, the RTA suffers from the drawback that relaxation times commonly employed are independent of initial conditions. We derive a variational principle for solutions to the...