Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session MC: Rarefied Gases |
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Chair: Michael Gallis, Sandia National Laboratories Room: 002A |
Tuesday, November 25, 2008 8:00AM - 8:13AM |
MC.00001: The Scaling of Atomistic Fluid Dynamics Simulations John Barber, Kai Kadau, Timothy Germann, Berni Alder In order to investigate the scaling properties of atomistic fluid dynamics simulations, we have performed a series of large-scale direct simulation Monte-Carlo simulations (containing up to 5.7 billion particles) of the Rayleigh-Taylor instability. The results, which include a wide range of length and time scales, suggest that such particle-based simulations exhibit the same scaling as predicted by the Navier-Stokes equation. In addition, a quantitative comparison with macroscopic Rayleigh-Taylor experimental results suggests that the results of micro-scale atomistic simulations can be scaled up to describe much larger systems, even in complex non-stationary flows. [Preview Abstract] |
Tuesday, November 25, 2008 8:13AM - 8:26AM |
MC.00002: Efficiency of the Sophisticated DSMC Algorithm M.A. Gallis, J.R. Torczynski Bird's sophisticated 2007 algorithm (DSMC07) is implemented in a two-dimensional Direct Simulation Monte Carlo (DSMC) code and compared to the standard 1994 algorithm (DSMC94) for multi-dimensional real-world rarefied-gas problems. Two test cases are examined. The first test case involves a typical DSMC problem, hypersonic flow over a wedge. The goal of this test case is to compare the algorithms when the same simulation parameters are used. The second test case involves a systematic analysis of the relative performance of the two algorithms for a real-world microsystem application that is out of reach for most DSMC codes. These comparisons confirm that when the discretization error tends to zero, both DSMC94 and DSMC07 produce results of the same accuracy. However, the two methods have a marked difference in their run times. For these cases, DSMC07 simulates 2-3 times as much physical time per processor-hour as DSMC94 at the same accuracy. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. [Preview Abstract] |
Tuesday, November 25, 2008 8:26AM - 8:39AM |
MC.00003: Low-variance direct Monte Carlo simulation of the Boltzmann transport equation in the relaxation-time approximation Gregg Radtke, Nicolas Hadjiconstantinou The relaxation-time approximation, known as the BGK model within the rarefied gas dynamics community, has recently found widespread application in various fields in connection to microscale and nanoscale science and technology. In this talk, we present an efficient particle method for simulating the Boltzmann transport equation in the relaxation-time approximation for application to problems where characteristic length scales are of the order of or smaller than the carrier (molecule, photon, phonon) mean free path. Our formulation's main advantage over existing particle methods--such as direct simulation Monte Carlo (DSMC)--is significantly reduced statistical uncertainty in low- signal (small deviation from equilibrium) problems, achieved by simulating only the deviation from equilibrium. Algorithms based on simulating the deviation from a global (absolute) and local equilibrium will be discussed and contrasted. [Preview Abstract] |
Tuesday, November 25, 2008 8:39AM - 8:52AM |
MC.00004: Solution of the Boltzmann Equation With Arbitrary Post-Collision Velocities A.B. Morris, P.L. Varghese, D.B. Goldstein We present a discrete velocity scheme which solves the Boltzmann equation and show numerical results for homogeneous relaxation problems. Although direct simulation of the Boltzmann equation can be efficient for transient problems, computational costs have limited its use. Traditional discrete velocity schemes require post-collision velocity pairs to lie precisely on the grid and additional constraints on mass, momentum, and energy further restrict the velocity grid to be uniform. A velocity interpolation algorithm enables us to select post-collision velocity pairs not restricted to those that lie on the grid. This algorithm allows arbitrary post-collision velocities as well as non-uniform grids to be used. On uniform grids many points contain negligible mass and it becomes computationally expensive to resolve the distribution function. By concentrating grid points near the center of mass velocity accurate solutions can be obtained efficiently. Comparisons between computed and reference solutions are shown for various grids, demonstrating correct relaxation rates and behavior of the macroscopic properties. [Preview Abstract] |
Tuesday, November 25, 2008 8:52AM - 9:05AM |
MC.00005: A multiscale simulation technique for moderate-Kn flows David Kessler, Elaine Oran, Carolyn Kaplan Gas flows for transition-regime Kundsen numbers (ratio of molecular mean-free-path to system size) and low fluid velocities occur in microscale devices operating at normal densities and pressures. Such flows are particularly difficult to simulate because there is no general and robust method that both applies and gives adequate answers in any reasonable computational time. Navier-Stokes methods (NS) are not accurate enough and particle based methods such as Direct Simulation Monte Carlo (DSMC) suffer from excessive noise in the solution. We are developing a multiscale simulation technique that combines use of NS and DSMC by replacing the constituitive relations in NS are by a viscous stress tensor and a heat flux vector obtained directly from independent, short-duration DSMC simulations. The approach is illustrated by computing a one-dimensional, planar Couette flow at moderate Knudsen numbers. We discuss computational issues encountered, such as data exchange between the continuum and molecular levels, statistical noise reduction, and the application of wall boundary conditions in the continuum-level solver. Problems associated with computing multidimensional flows are briefly discussed. [Preview Abstract] |
Tuesday, November 25, 2008 9:05AM - 9:18AM |
MC.00006: A DSMC-based variance reduction formulation for low-signal flows Husain Al-Mohssen, Nicolas Hadjiconstantinou Particle methods for simulating the Boltzmann equation become prohibitively expensive in low-signal (e.g. low-speed) flows due to the large statistical uncertainty associated with the sampling of hydrodynamic quantities. We present a variance reduction technique for use in such flows (typically encountered in small-scale applications) that does not require modification of the DSMC procedure. The proposed method is based on the observation that low-signal flows are characterized by small deviations from well-defined equilibrium states and thus lend themselves naturally to variance reduction approaches. The present formulation uses an ``auxiliary'' simulation to describe a judiciously chosen equilibrium state using the same particle data samples as the non-equilibrium simulation. Subtracting the equilibrium hydrodynamic fields from the ones obtained by the non-equilibrium simulation significantly reduces the statistical uncertainty of the latter because the two calculations are correlated. We find that, similarly to previous variance reduction approaches, the present method exhibits statistical uncertainty that scales with the deviation from equilibrium, making the simulation of arbitrarily small deviations from equilibrium possible. [Preview Abstract] |
Tuesday, November 25, 2008 9:18AM - 9:31AM |
MC.00007: Analysis of non-equilibrium multi-species mixing based on Boltzmann kinetic theory Prakash Vedula, Rodney O. Fox In many applications of non-equilibrium flows relevant to design of micro-fluidic devices and spacecraft propulsion systems, where standard continuum field descriptions of multi-species mixing break down (when Knudsen number is not negligible), descriptions based on fundamental kinetic theory can be insightful. We use Boltzmann kinetic theory to obtain a statistical description of macroscopic system properties of multi-species mixing, using particle distribution functions for each species, which are governed by a system of coupled, nonlinear, integro-differential Boltzmann equations involving full collision operators. Formidable challenges involved in the computational treatment of full collision operators, consisting of multi-dimensional integrals, are addressed through an efficient quadrature-based moment method which not only preserves collision invariants but is also capable of describing general far-from equilibrium behavior. In this method, discrete representations of the particle distribution functions for each species are sought by accounting for generalized moment contributions due to full collision operators, which can be evaluated analytically via multinomial expansions. Fundamental behavior relevant to exchange of momentum, energy and generalized stresses among inert multiple species undergoing mixing, with and without the presence of spatial inhomogeneities, will be analyzed using this method. [Preview Abstract] |
Tuesday, November 25, 2008 9:31AM - 9:44AM |
MC.00008: Knudsen Diffusion in Nanochannels Patrick Huber, Simon Gruener, Stefan Bommer Measurements on helium and argon gas flow through an array of parallel, linear channels of $12$~nm diameter and $200$~$\rm\mu$m length in a single crystalline silicon membrane reveal a Knudsen diffusion type transport from $10^{\rm 2}$ to $10^{\rm 7}$ in Knudsen number $Kn$. The classic scaling prediction for the transport diffusion coefficient on temperature and mass of diffusing species, $D_{\rm He}\propto \sqrt{T}$ is confirmed over a $T$-range from 40~K to 300~K for He and for the ratio of $D_{\rm He}/D_{\rm Ar} \propto \sqrt{m_{\rm Ar}/m_{\rm He}}$. Deviations of the channels from a cylindrical form, resolved with electron microscopy down to subnanometer scales, quantitatively account for a reduced diffusivity as compared to Knudsen diffusion in ideal tubular channels. The membrane permeation experiments are described over 10 orders of magnitude in $Kn$, encompassing the transition flow regime, by the unified flow model of Beskok and Karniadakis. Simon Gruener and Patrick Huber, Phys. Rev. Lett. 100, 064502 (2008). [Preview Abstract] |
Tuesday, November 25, 2008 9:44AM - 9:57AM |
MC.00009: Scattering of gas molecules on the films of vertically aligned single-walled carbon nanotubes Ikuya Kinefuchi, Yushi Harada, Jumpei Kawasaki, Kei Ishikawa, Junichiro Shiomi, Shu Takagi, Shigeo Maruyama, Yoichiro Matsumoto The scattering process of helium molecules on vertically aligned single-walled carbon nanotubes (VA-SWNTs) has been investigated using the molecular beam technique. The energy accommodation coefficients for VA-SWNT films on quartz substrates are remarkably high at room temperature compared to those for the bare substrates, demonstrating the effectiveness of the surface modification technique with VA-SWNT films for enhancing the energy transfer between gas molecules and surfaces in rarefied gas flows. The thickness dependence of the accommodation coefficient suggests that helium molecules penetrate the films because of their high porosity and suffer multiple collisions with carbon nanotubes. The less effective energy accommodation at elevated temperatures implies the significant decrease in the trapping probability of helium molecules on carbon nanotube surfaces during each collision because of the small adsorption potential well, which is comparable to the thermal energy at room temperature. [Preview Abstract] |
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