Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-10T17:44:29.415Z Has data issue: false hasContentIssue false
  • English
  • Français

Unified Gas Kinetic Scheme and Direct Simulation Monte Carlo Computations of High-Speed Lid-Driven Microcavity Flows

Published online by Cambridge University Press:  03 June 2015

Vishnu Venugopal  and
Sharath S. Girimaji
Vishnu Venugopal
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX-77843, United States of America
Sharath S. Girimaji*
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX-77843, United States of America
*
*Corresponding author. Email addresses: vishnuv@tamu.edu (V. Venugopal), girimaji@tamu.edu (S. S. Girimaji)
Get access

Abstract

Accurate simulations of high-speed rarefied flows present many physical and computational challenges. Toward this end, the present work extends the Unified Gas Kinetic Scheme (UGKS) to a wider range of Mach and Knudsen numbers by implementing WENO (Weighted Essentially Non-Oscillatory) interpolation. Then the UGKS is employed to simulate the canonical problem of lid-driven cavity flow at high speeds. Direct Simulation Monte Carlo (DSMC) computations are also performed when appropriate for comparison. The effect of aspect ratio, Knudsen number and Mach number on cavity flow physics is examined leading to important insight.

Keywords

82C4076P0465C05UGKSDSMClid driven cavitykinetic theoryKnudsen number
Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 5 , May 2015 , pp. 1127 - 1150
Copyright
Copyright © Global-Science Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Bertin, J. J. and Cummings, R. M., Critical Hypersonic Aerothermodynamic Phenomena, Annual Review of Fluid Mechanics 38: 129–157, Jan 2006.Google Scholar
[2]Xu, K. and Huang, J. C., A unified gas-kinetic scheme for rarefied and continuum flows, J. Comp. Phy. 229, 7747–7764, 2010.Google Scholar
[3]Shakhov, E.M., Generalization of the Krook kinetic equation, Fluid Dyn. 3: 95, 1968.Google Scholar
[4]Bhatnagar, P.L., Gross, E.P., Krook, M., A model for collision processes in gases I: small amplitude processes in charged and neutral one-component systems, Phys. Rev. 94: 511525, 1954.CrossRefGoogle Scholar
[5]Yang, J.Y., Huang, J.C., Rarefied flow computations using non-linear model Boltzmann equations, J. Comput. Phys. 120: 323339, 1995.Google Scholar
[6]Shu, Chi-Wang, Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory schemes for hyperbolic conservation laws, NASA/CR-97–206253, ICASE Report No. 97–65, 1997Google Scholar
[7]Yamaleev, N. K., Carpenter, M. H., Higher order energy stable WENO schemes, 47th AIAA Aerospace Sciences Meeting, Orlando, FL, USA, 2009.Google Scholar
[8]Leer, B. Van, Towards the ultimate conservative difference scheme V. A second order sequel to Godunov’s method, J. Comp. Phys. 32: 101136, 1979.Google Scholar
[9]Bird, G. A., Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford Science Publications, 1994.Google Scholar
[10]Xu, K., Gas-Kinetic Schemes for Unsteady Compressible Flow Simulations, von Karman Institute for Fluid Dynamics, Lecture Series 1998–03, 29th Computational Fluid Dynamics, (Feb. 23–27, 1998).Google Scholar
[11]Guo, Z., Xu, K., Wang, Ruijie, Discrete unified gas kinetic scheme for fluid dynamics: I. Isothermal smooth flows, May 2013.Google Scholar
[12]Kerimo, J. and Girimaji, S. S., DNS of decaying isotropic turbulence with Boltzmann BGK approach, J. Turb. 46 (8): 1–16, 2007.Google Scholar
[13]Kumar, G. and Girimaji, S. S., WENO-enhanced Gas Kinetic Method for highly compressible transition and turbulence simulations, J. Comp. Phys. 234 (1): 499–523, 2013.Google Scholar
[14]Prendergast, K. H., Xu, K., Numerical hydrodynamics from gas kinetic theory, J. Comp. Phys. 109(1): 5366, 1993.Google Scholar
[15]Shizgal, B., A Gaussian quadrature procedure for use in the solution of the Boltzmann equation and related problems, J. Comp. Phys. 41: 309328, 1981. doi:10.1016/0021–9991(81)90099–1Google Scholar
[16]Mohammadzadeh, A., Roohi, E., Niazmand, H., A Parallel DSMC Investigation of Monatomic/Diatomic Gas Flows in a Micro/Nano Cavity, Numerical Heat Transfer, Part A 63:4, 305–325, 2013.CrossRefGoogle Scholar
[17]Bartel, T. J., Sterk, T. M., Payne, J. L., Preppernau, B., DSMC Simulation of Nozzle Expansion Flow Fields, 6th AIAA/ASME Joint Thermophysics and Heat Transfer Conference June 20–23, 1994.Google Scholar
[18]Wang, Z., Bao, L., Tong, B., Rarefaction criterion and non-Fourier heat transfer in hypersonic rarefied flows, Physics of Fluids 22, 126103, 2010.Google Scholar
[19]Lewis, E.E., Miller, W.F. Jr., Computational Methods in Neutron Transport Theory, Wiley, 1984.Google Scholar
[20]Naris, S. and Valougeorgis, D., The driven cavity flow over the whole range of the Knudsen number, Physics of Fluids 17, 097106, 2005Google Scholar
[21]Varoutis, S., Valougeorgis, D., Sharipov, F., Application of the integro-moment method to steady-state two-dimensional rarefied gas flows subject to boundary induced discontinuities, J. Comp. Phys. 227: 6272–6287, 2008.CrossRefGoogle Scholar
[22]Guo, Z., Xu, K., Wang, R., Discrete unified gas kinetic scheme for all Knudsen number flows: Low-speed isothermal case, Physical Review E 88, 033305, 2013.CrossRefGoogle ScholarPubMed