Publication Cover
Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 72, 2017 - Issue 6
155
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

A simple gas kinetic scheme for simulation of 3D incompressible thermal flows

, , &
Pages 450-468 | Received 04 Sep 2017, Accepted 14 Nov 2017, Published online: 14 Dec 2017

References

  • K. Xu, Gas-Kinetic Schemes for Unsteady Compressible Flow Simulations. Brussels: van Kareman Institute for Fluid Dynamics Lecture series 1998-03, 1998.
  • R. Yuan, C. Zhong, and H. Zhang, “An immersed-boundary method based on the gas kinetic BGK scheme for incompressible viscous flow,” J. Comput. Phys., vol. 296, pp. 184–208, 2015.
  • K. Xu, M. Mao, and L. Tang, “A multidimensional gas-kinetic BGK scheme for hypersonic viscous flow,” J. Comput. Phys., vol. 203, pp. 405–421, 2005.
  • G. May, B. Srinivasan, and A. Jameson, “An improved gas-kinetic BGK finite-volume method for three-dimensional transonic flow,” J. Comput. Phys., vol. 220, pp. 856–878, 2007.
  • J. Jiang and Y Qian, “Implicit gas-kinetic BGK scheme with multigrid for 3D stationary transonic high-Reynolds number flows,” Comput. Fluids, vol. 66, pp. 21–28, 2012.
  • L. M. Yang, C. Shu, and J. Wu, “A simple distribution function-based gas-kinetic scheme for simulation of viscous incompressible and compressible flows,” J. Comput. Phys., vol. 274, pp. 611–632, 2014.
  • Y. Sun, C. Shu, C. J. Teo, Y. Wang, and L. M. Yang, “Explicit formulations of gas-kinetic flux solver for simulation of incompressible and compressible viscous flows,” J. Comput. Phys., vol. 300, pp. 492–519, 2015.
  • K. Xu, “BGK-based scheme for multicomponent flow calculations,” J. Comput. Phys., vol. 134, pp. 122–133, 1997.
  • Y. S. Lian and K. Xu, “A gas-kinetic scheme for multimaterial flows and its application in chemical reactions,” J. Comput. Phys., vol. 163, pp. 349–375, 2000.
  • L. M. Yang, C. Shu, J. Wu, and Y. Wang, “Numerical simulation of flows from free molecular regime to continuum regime by a DVM with streaming and collision processes,” J. Comput. Phys., vol. 306, pp. 291–310, 2016.
  • J. C. Huang, K. Xu, and P. Yu, “A unified gas-kinetic scheme for continuum and rarefied flows II: multi-dimensional cases,” Commun. Comput. Phys., vol. 3, pp. 662–690, 2012.
  • Z. Guo, R. Wang, and K. Xu, “Discrete unified gas kinetic scheme for all Knudsen number flows: II. Thermal Compressible case,” Phys. Rev. E, vol. 91, pp. 033313, 2015.
  • E. F. Toro, M. Spruce, and W. Speares, “Restoration of the contact surface in the HLL-Riemann solver,” Shock Wave, vol. 4, pp. 25–34, 1994.
  • R. Verzicco and P. Orlandi, “A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates,” J. Comput. Phys., vol. 123, pp. 402–414, 1996.
  • K. Zamzamian and S. E. Razavi, “Multidimensional upwinding for incompressible flows based on characteristics,” J. Comput. Phys., vol. 227, pp. 8699–8713, 2008.
  • C. B. Lee and S. Wang, “Study of the shock motion in a hypersonic shock system/turbulent boundary layer interaction,” Exp. Fluids, vol. 19, pp. 143–149, 1995.
  • L. M. Yang, C. Shu, and J. Wu, “A hybrid lattice Boltzmann flux solver for simulation of viscous compressible flows,” Adv. Appl. Math. Mech., vol. 8, pp. 887–910, 2016.
  • S. Chen, C. Jin, C. Li, and Q. Cai, “Gas-kinetic scheme with discontinuous derivative for low speed flow computation,” J. Comput. Phys., vol. 230, pp. 2045–2059, 2011.
  • K. Xu, “A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method,” J. Comput. Phys., vol. 171, pp. 289–335, 2001.
  • L. Tang, “Progress in gas-kinetic upwind schemes for the solution of Euler/Navier-Stokes equations-I: Overview,” Comput. Fluids, vol. 56, pp. 39–48, 2012.
  • G. Kumar, S. S. Girimaji, and J. Kerimo, “WENO-enhanced gas-kinetic scheme for direct simulations of compressible transition and turbulence,” J. Comput. Phys., vol. 234, pp. 499–523, 2013.
  • L. Pan and K. Xu, “Generalized coordinate transformation and gas-kinetic scheme,” J. Comput. Phys., vol. 287, pp. 207–225, 2015.
  • M. Su, K. Xu, and M. S. Ghidaoui, “Low-speed flow simulation by the gas-kinetic scheme,” J. Comput. Phys., vol. 150, pp. 17–39, 1999.
  • K. Xu and X. He, “Lattice Boltzmann method and gas-kinetic BGK scheme in the low-Mach number viscous flow simulations,” J. Comput. Phys., vol. 190, pp. 100–117, 2003.
  • Z. Guo, H. Liu, L. S. Luo, and K. Xu, “A comparative study of the LBE and GKS methods for 2D near incompressible laminar flows,” J. Comput. Phys., vol. 227, pp. 4955–4976, 2008.
  • K. Xu and S. H. Lui, “Rayleigh-Bénard simulation using the gas-kinetic Bhatnagar-Gross-Krook scheme in the incompressible limit,” Phys. Rev. E, vol. 60, pp. 464–470, 1999.
  • L. M. Yang, C. Shu, J. Wu, N. Zhao, and Z. L. Lu, “Circular function-based gas-kinetic scheme for simulation of inviscid compressible flows,” J. Comput. Phys., vol. 255, pp. 540–557, 2013.
  • L. M. Yang, C. Shu, and J. Wu, “A three-dimensional explicit sphere function-based gas-kinetic flux solver for simulation of inviscid compressible flows,” J. Comput. Phys., vol. 295, pp. 322–339, 2015.
  • L. M. Yang, C. Shu, Y. Wang, and Y. Sun, “Development of discrete gas kinetic scheme for simulation of 3D viscous incompressible and compressible flows,” J. Comput. Phys., vol. 319, pp. 129–144, 2016.
  • L. M. Yang, C. Shu, W. M. Yang, Y. Wang, and J. Wu, “An immersed boundary-simplified sphere function-based gas kinetic scheme for simulation of 3D incompressible flows,” Phys. Fluids, vol. 29, pp. 083605, 2017.
  • Y. Wang, C. Shu, C. J. Teo, and L. M. Yang, “An efficient immersed boundary-lattice Boltzmann flux solver for simulation of 3D incompressible flows with complex geometry,” Comput. Fluids, vol. 124, pp. 54–66, 2016.
  • D. Singh, B. Premachandran, and S. Kohli, “Numerical simulation of the jet impingement cooling of a circular cylinder,” Numer. Heat Transfer A, vol. 64, pp. 153–185, 2013.
  • Z. Jing, M. J. Ni, and Z. H. Wang, “Numerical study of MHD natural convection of liquid metal with wall effects,” Numer. Heat Transfer A, vol. 64, pp. 676–693, 2013.
  • P. Ding and D. L. Sun, “Pressure-based segregated solver for incompressible flow on unstructured grids,” Numer. Heat Transfer B, vol. 64, pp. 460–479, 2013.
  • H. Chen, K. Li, Y. Yang, and S. Wang, “A dimension splitting method for 3-D incompressible thermal flow,” Numer. Heat Transfer B, vol. 68, pp. 336–365, 2015.
  • S. M. Kim and K. Y. Kim, “Microcooling system with impinging jets and a stalactite structure,” Numer. Heat Transfer A, vol. 69, pp. 1376–1389, 2016.
  • G. Liang, X. Mu, Y. Guo, and S. Shen, “Flow and heat transfer during a single drop impact on a liquid film,” Numer. Heat Transfer B, vol. 69, pp. 575–582, 2016.
  • X. He, S. Chen, and G. D. Doolen, “A novel thermal model for the lattice Boltzmann method in incompressible limit,” J. Comput. Phys., vol. 146, pp. 282–300, 1998.
  • Y. Peng, C. Shu, and Y. T. Chew, “A 3D incompressible thermal lattice Boltzmann model and its application to simulate natural convection in a cubic cavity,” J. Comput. Phys., vol. 193, pp. 260–274, 2004.
  • C. N. Azwadi and S. Syahrullail, “A three-dimension double-population thermal lattice BGK model for simulation of natural convection heat transfer in a cubic cavity,” WSEAS Trans. Math., vol. 8, pp. 561–570, 2009.
  • Z. Guo, C. Zheng, B. Shi, and T. S. Zhao, “Thermal lattice Boltzmann equation for low Mach number flows: decoupling model,” Phys. Rev. E, vol. 75, pp. 036704, 2007.
  • Z. Guo, B. Shi, and C. Zheng, “A coupled lattice BGK model for the Boussinesq equations,” Int. J. Numer. Method Fluids, vol. 39, pp. 325–342, 2002.
  • S. Chen and G. D. Doolen, “Lattice Boltzmann method for fluid flows,” Annu. Rev. Fluid Mech., vol. 30, pp. 329–364, 1998.
  • S. Succi, The Lattice Boltzmann Equation: For Fluid Dynamics and Beyond, Chap. 14. New York: Oxford University Press, 2001.
  • T. Fusegi, J. M. Hyun, K. Kuwahara, and B. Farouk, “A numerical study of three-dimensional natural convection in a differentially heated cubical enclosure,” Int. J. Heat Mass Transfer, vol. 34, pp. 1543–1557, 1991.
  • E. Tric, G. Labrosse, and M. Betrouni, “A first incursion into the 3D structure of natural convection of air in a differentially heated cubic cavity, from accurate numerical solutions,” Int. J. Heat Mass Transfer, vol. 43, pp. 4043–4056, 2000.
  • D. C. Lo, D. L. Young, and K. Murugesan, “GDQ method for natural convection in a cubic cavity using velocity-vorticity formulation,” Numer. Heat Transfer B, vol. 48, pp. 363–386, 2005.
  • B. A. V. Bennett and J. Hsueh, “Natural convection in a cubic cavity: Implicit numerical solution of two benchmark problems,” Numer. Heat Transfer A, vol. 50, pp. 99–123, 2006.
  • Y. Wang, C. Shu, C. J. Teo, J. Wu, and L. M. Yang, “Three-dimensional lattice Boltzmann flux solver and its applications to incompressible isothermal and thermal flows,” Commun. Comput. Phys., vol. 18, pp. 593–620, 2015.
  • J. Pallares, I. Cuesta, F. X. Grau, and F. Giralt, “Natural convection in a cubical cavity heated from below at low Rayleigh numbers,” Int. J. Heat Mass Transfer, vol. 39, pp. 3233–3247, 1996.
  • A. Kumar Santra, D. Misra, and S. Ray, “Analysis of laminar natural convection from a discrete isothermal flush heater mounted on the side wall of a partially open rectangular enclosure,” Numer. Heat Transfer A, vol. 29, pp. 211–225, 1996.
  • I. Sezai and A. A. Mohamad, “Natural convection from a discrete heat source on the bottom of a horizontal enclosure,” Int. J. Heat Mass Transfer, vol. 43, pp. 2257–2266, 2000.
  • A. R. Rahmati and M. Ashrafizaadeh, “A generalized lattice Boltzmann method for three-dimensional incompressible fluid flow simulation,” J. Appl. Fluid Mech., vol. 2, pp. 71–95, 2009.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.