The nonlinear Burnett coeecients are the Tay-lor series coeecients for the functional dependence describing how the Thermodynamic Flux responds to a Thermodynamic Force acting on a uid. Ernst et. al. computed the functional dependence exactly for a hard disk/sphere uid (a uid made up of idealised billiard balls) undergoing shear ow, and found that the relationship was non-analytic, i.e. that th...

A derivation of hydrodynamics from the Boltzmann kinetic equation is the classical problem of physical kinetics. The Chapman-Enskog (CE) method [1] gives, in principle, a possibility to compute a solution as a formal series in powers of Knudsen number e (where e is a ratio between the mean free path of a particle and the scale of variations of hydrodynamic quantities, density, mean flux, and te...

Particular solutions that correspond to inhomogeneous driving terms in the linearized Boltzmann equation for the case of a binary mixture of rigid spheres are reported. For flow problems (in a plane channel) driven by pressure, temperature, and density gradients, inhomogeneous terms appear in the Boltzmann equation, and it is for these inhomogeneous terms that the particular solutions are devel...

* Present address: Applied Mathematics Department, Brookhaven National Laboratory, Upton, New York. • See, for instance, L. Landau and E. Lifshitz, Fluid Mechanics (Addison-Wesley Publishing Co., Inc., Reading, Mass., 1959). scribed by the classical theory of Stokes and Kirchoff. • This theory is, of course, based on the Navier-Stokes equations. However, for high-frequency sound propagation in ...

We apply the projection operator formalism to the problem of determining the asymptotic behavior of the lattice BGK equation in the hydrodynamic limit. As an alternative to the more usual Chapman-Enskog expansion, this approach offers many benefits. Most remarkably, it produces absolutely exact, though non-Markovian, hydrodynamic difference equations as an intermediate step. These are accurate ...