1996/12/09 by Xiaowen Shan · 2 citations
Engineering · Physics and Astronomy · #Boundary value problem #Classical mechanics #Convection #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis #Heat transfer #Lattice Boltzmann Simulation Studies #Lattice Boltzmann methods #Mechanics #Natural convection #Nusselt number #Physics #Rayleigh number #Rayleigh scattering #Reynolds number #comp-gas #nlin.CG
paper · pdf · doi:10.1103/physreve.55.2780
20 pages, REVTEX
arxiv created 1996/12/09 · openalex publication_date 1997/03/01 · arxiv updated 2016/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Rayleigh-B'enard convection is numerically simulated in two and three dimensions using a recently developed two-component lattice Boltzmann equation (LBE) method. The density field of the second component, which evolves according to the advection-diffusion equation of a passive scalar, is used to simulate the temperature field. A body force proportional to the temperature is applied, and the system satisfies the Boussinesq equation except for a slight compressibility. A no-slip, isothermal boundary condition is imposed in the vertical direction, and periodic boundary conditions are used in horizontal directions. The critical Rayleigh number for the onset of the Rayleigh-B'enard convection agrees with the theoretical prediction. As the Rayleigh number is increased higher, the steady two-dimensional convection rolls become unstable. The wavy instability and aperiodic motion observed, as well as the Nusselt number as a function of the Rayleigh number, are in good agreement with experimental observations and theoretical predictions. The LBE model is found to be efficient, accurate, and numerically stable for the simulation of fluid flows with heat and mass transfer.