Application of Gaussian Moment Closures to Three-Dimensional Micro-Scale Flows.

摘要

A parallel, implicit, adaptive mesh refinement (AMR), finite-volume scheme is described for the solution of the standard and regularized Gaussian moment closures on three-dimensional, multi-block, body-fitted, hexahedral meshes. The standard Gaussian closure has been shown to accurately predict non-equilibrium phenomena at moderate Knudsen numbers through an anisotropic treatment of pressure. The regularized closure builds on these advantages and includes the effects of non-equilibrium heat transfer by means of a first-order correction to the standard Gaussian closure. The combined moment closure treatment / numerical method is applied to the prediction of three-dimensional, non-equilibrium, micro-scale, gaseous flows. Unlike other regularized moment closures, the underlying closure is the standard maximum-entropy Gaussian closure which provides a fully-realizable and strictly hyperbolic description of non-equilibrium gaseous flows that is valid from the continuum limit, through the transition regime, and up to the free-molecular flow limit. The proposed finite-volume scheme uses Riemann-solver-based flux functions and limited linear reconstruction to provide accurate and monotonic solutions, even in the presence of large solution gradients and/or under-resolved solution content. A rather effective and highly scalable parallel implicit time-marching scheme based on a Jacobian-free inexact Newton-Krylov-Schwarz (NKS) approach with additive Schwarz preconditioning and domain partitioning following from the multi-block AMR mesh is used to obtain solutions to the non-linear ordinary-differential equations that result from finite-volume spatial discretization procedure. Details are given of the standard and regularized Gaussian closure, extensions for diatomic gases, and slip-flow boundary treatment. Numerical results for several canonical flow problems demonstrate the potential of the closures, that when combined with an efficient parallel solution method, provide an effective means for accurately predicting a range of fully three-dimensional non-equilibrium gaseous flow behavior.