This paper is concerned with the Navier-Stokes limit of a class globally hyperbolic moment equations from Boltzmann equation. we show that can be formally derived for various different collision mechanisms. Furthermore, formal justified rigorously by using an energy method. It should noted are in non-conservative form and do not have convex entropy function, therefo...

This dissertation presents a step towards high-order methods for continuum-transition flows. In order to achieve maximum accuracy and efficiency for numerical methods on a distorted mesh, it is desirable that both governing equations and corresponding numerical methods are in some sense compact. We argue our preference for a physical model described solely by first-order partial differential eq...

We present detailed comparisons between high-resolution Monte Carlo simulation (MCS) and low-order numerical solutions of stochastic moment equations (SMEs) for the first and second statistical moments of pressure. The objective is to quantify the difference between the predictions obtained from MCS and SME. Natural formations with high permeability variability and large spatial correlation sca...

A novel adaptive mesh refinement (AMR) strategy based on the moment-of-fluid (MOF) method for volume-tracking of evolving interfaces is presented. Moment-offluid method is a new interface reconstruction and volume advection method using volume fractions as well as material centroids. The mesh refinement criterion is based on the deviation of the actual centroid obtained by interface reconstruct...