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On a two-relaxation-time D2Q9 lattice Boltzmann model for the Navier–Stokes equations

Author

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  • Zhao, Weifeng
  • Wang, Liang
  • Yong, Wen-An

Abstract

In this paper, we are concerned with the stability of some lattice kinetic schemes. First, we show that a recently proposed lattice kinetic scheme is a two-relaxation-time model different from those in the literature. Second, we analyze the stability of the model by verifying the Onsager-like relation. In addition, a necessary stability criterion for hyperbolic relaxation systems is adapted to the lattice Boltzmann method. As an application of this criterion, we find some necessary stability conditions for a previously proposed lattice kinetic scheme. Numerical experiments are conducted to validate the necessary stability conditions.

Suggested Citation

  • Zhao, Weifeng & Wang, Liang & Yong, Wen-An, 2018. "On a two-relaxation-time D2Q9 lattice Boltzmann model for the Navier–Stokes equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1570-1580.
    • Handle: RePEc:eee:phsmap:v:492:y:2018:i:c:p:1570-1580
    DOI: 10.1016/j.physa.2017.11.082
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    Citations

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    Cited by:

    1. Ahmadi Balootaki, Azam & Karimipour, Arash & Toghraie, Davood, 2018. "Nano scale lattice Boltzmann method to simulate the mixed convection heat transfer of air in a lid-driven cavity with an endothermic obstacle inside," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 681-701.
    2. Karimipour, Arash & D’Orazio, Annunziata & Goodarzi, Marjan, 2018. "Develop the lattice Boltzmann method to simulate the slip velocity and temperature domain of buoyancy forces of FMWCNT nanoparticles in water through a micro flow imposed to the specified heat flux," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 729-745.
    3. Goodarzi, Marjan & D’Orazio, Annunziata & Keshavarzi, Ahmad & Mousavi, Sayedali & Karimipour, Arash, 2018. "Develop the nano scale method of lattice Boltzmann to predict the fluid flow and heat transfer of air in the inclined lid driven cavity with a large heat source inside, Two case studies: Pure natural ," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 210-233.
    4. Safaei, Mohammad Reza & Karimipour, Arash & Abdollahi, Ali & Nguyen, Truong Khang, 2018. "The investigation of thermal radiation and free convection heat transfer mechanisms of nanofluid inside a shallow cavity by lattice Boltzmann method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 515-535.

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