Hydrodynamics beyond Navier-Stokes: Exact Solution to the Lattice Boltzmann Hierarchy

Hydrodynamics beyond Navier-Stokes: exact solution to the lattice Boltzmann hierarchy.

The exact solution to the hierarchy of nonlinear lattice Boltzmann (LB) kinetic equations in the stationary planar Couette flow is found at nonvanishing Knudsen numbers. A new method of solving LB kinetic equations which combines the method of moments with boundary conditions for populations enables us to derive closed-form solutions for all higher-order moments. A convergence of results sugges...

Entropic lattice Boltzmann representations required to recover Navier-Stokes flows.

There are two disparate formulations of the entropic lattice Boltzmann scheme: one of these theories revolves around the analog of the discrete Boltzmann H function of standard extensive statistical mechanics, while the other revolves around the nonextensive Tsallis entropy. It is shown here that it is the nonenforcement of the pressure tensor moment constraints that lead to extremizations of e...

An exact analytical solution to the extended Navier - Stokes equations using the Lambert W function

Micro channel gas flows are of importance in a range Micro Electro Mechanical Systems (MEMS). Due to the confined geometry of the channel, the mean free path of the gas can be comparable to the characteristic length of the micro channel, leading to slip-like flow behavior and strong diffusion-enhanced transport of mass and momentum. The Extended Navier Stokes Equations (ENSE) have successfully ...

Alternative and Explicit Derivation of the Lattice Boltzmann Equation for the Unsteady Incompressible Navier-Stokes Equation

An H-Theorem for the Lattice Boltzmann Approach to Hydrodynamics

– The lattice Boltzmann equation can be viewed as a discretization of the continuous Boltzmann equation. Because of this connection it has long been speculated that lattice Boltzmann algorithms might obey an H-theorem. In this letter we prove that usual nine-velocity models do not obey an H-theorem but models that do obey an H-theorem can be constructed. We consider the general conditions a lat...