On the dependence of the Navier–Stokes equations on the distribution of molecular velocities

Abstract

In this work we introduce a completely general Chapman Enskog procedure in which we divide the local distribution into an isotropic distribution with anisotropic corrections. We obtain a recursion relation on all integrals of the distribution function required in the derivation of the moment equations. We obtain the hydrodynamic equations in terms only of the first few moments of the isotropic part of an arbitrary local distribution function.The incompressible limit of the equations is completely independent of the form of the isotropic part of the distribution, whereas the energy equation in the compressible case contains an additional contribution to the heat flux. This additional term was also found by Boghosian and by Potiguar and Costa [2,3] in the derivation of the Navier Stokes equations for Tsallis thermostatistics, and is the only additional term allowed by the Curie principle.

From the Boltzmann equation to fluid mechanics on a manifold

“…We work in D dimensions to make the role of dimensionality explicit. We assume a Maxwell-Boltzmann equilibrium, although it is sufficient to assume that the local equilibrium distribution is Gallilean invariant and isotropic [6].…”