Szoke, Abraham | Search NASA

DOE OSTI2015

The Boltzmann equation in the difference formulation

First we recall the assumptions that are needed for the validity of the Boltzmann equation and for the validity of the compressible Euler equations. We then present the difference formulation of these equations and make a connection with the time-honored Chapman - Enskog expansion. We discuss the hydrodynamic limit and calculate the thermal conductivity of a monatomic gas, using a simplified approximation for the collision term. Our formulation is more consistent and simpler than the traditional derivation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

A Variational Method for Interpolation Between Zone Centers in 2-D Geometry

Radiation-hydrodynamics codes are often based on a zone centered discretization strategy for the hydrodynamics, while transport requires a higher order interpolated treatment of the material state variable to produce a correct solution in optically thick media. In this paper, we use a variational method to generalize a previously developed 1-D interpolation method to 2-D geometries. While our interpolation method was developed to handle the gradient source term for thermal photons in the Difference Formulation, it may also be useful for the generation of an accurate zone centered discretization for diffusion methods. We provide a detailed description of the 2-D interpolation method and how it relates to the 1-D method that was developed earlier. We also discuss how this interpolation strategy can be extended to 3-D, but do not work through the details.

97 MATHEMATICS AND COMPUTING↗