Lattice Boltzmann simulation of natural convection in a square cavity

J. Onishi, Y. Chen, H. Ohashi

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25 Citations (Scopus)


In this paper, we describe the development of a lattice Boltzmann scheme for incompressible thermohydrodynamics. Being based on kinetic theory, the scheme simulates macroscopic fluid flows and heat transfers with the use of distribution functions. A systematic derivation of the lattice Boltzmann scheme from the continuous Boltzmann equation is discussed in details. We find that a 5-velocity model can be employed to simulate heat transfer in such a case where the viscous and compressive heating effects are negligible. As a benchmark, numerical simulations of natural convection in a square cavity are carried out. Through the results, the scheme is found to have a second-order convergence rate. In addition, the scheme is verified to be as accurate as conventional methods over a wide range of Rayleigh numbers.

Original languageEnglish
Pages (from-to)53-62
Number of pages10
JournalJSME International Journal, Series B: Fluids and Thermal Engineering
Issue number1
Publication statusPublished - 2001 Feb


  • Computational fluid dynamics Benchmark solution
  • Lattice Boltzmann method
  • Thermohydrodynamics


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