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Towards the development of a multiscale, multiphysics method for the simulation of rarefied gas flows

Published online by Cambridge University Press:  02 August 2010

DAVID A. KESSLER ,
ELAINE S. ORAN  and
CAROLYN R. KAPLAN
DAVID A. KESSLER*
Affiliation:
Laboratory for Computational Physics and Fluid Dynamics, US Naval Research Laboratory, Washington, DC 20375, USA
ELAINE S. ORAN
Affiliation:
Laboratory for Computational Physics and Fluid Dynamics, US Naval Research Laboratory, Washington, DC 20375, USA
CAROLYN R. KAPLAN
Affiliation:
Laboratory for Computational Physics and Fluid Dynamics, US Naval Research Laboratory, Washington, DC 20375, USA
*
†Email address for correspondence: dakessle@lcp.nrl.navy.mil
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Abstract

We introduce a coupled multiscale, multiphysics method (CM3) for solving for the behaviour of rarefied gas flows. The approach is to solve the kinetic equation for rarefied gases (the Boltzmann equation) over a very short interval of time in order to obtain accurate estimates of the components of the stress tensor and heat-flux vector. These estimates are used to close the conservation laws for mass, momentum and energy, which are subsequently used to advance continuum-level flow variables forward in time. After a finite time interval, the Boltzmann equation is solved again for the new continuum field, and the cycle is repeated. The target applications for this type of method are transition-regime gas flows for which standard continuum models (e.g. Navier–Stokes equations) cannot be used, but solution of Boltzmann's equation is prohibitively expensive. The use of molecular-level data to close the conservation laws significantly extends the range of applicability of the continuum conservation laws. In this study, the CM3 is used to perform two proof-of-principle calculations: a low-speed Rayleigh flow and a thermal Fourier flow. Velocity, temperature, shear-stress and heat-flux profiles compare well with direct-simulation Monte Carlo solutions for various Knudsen numbers ranging from the near-continuum regime to the transition regime. We discuss algorithmic problems and the solutions necessary to implement the CM3, building upon the conceptual framework of the heterogeneous multiscale methods.

JFM classification

Mathematical Foundations: Computational methods Compressible Flows: Gas dynamics Rarefied Gas Flow: Kinetic theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 661 , 25 October 2010 , pp. 262 - 293
Copyright
Copyright © Cambridge University Press 2010

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