Lattice Boltzmann Simulation of Transient Natural Convection in a Staggered Cavity with Four Vertically Heated Walls

Abstract:

The work in this manuscript deals with the numerical simulation of natural convection in a staggered cavity with the help of a recently developed two-dimensional double Multiple-Relaxation-Time (MRT) thermal Lattice Boltzmann method (LBM). In the last decade, there has been a rapid rise in the development of Lattice Boltzmann methods. However, its application in the simulation of natural convection from a staggered cavity has been carried out for the first time in this study. A careful undermining into the existing literature of heat and mass transfer reveal that study of natural convections in cross-sectional cavities is notably absent. Therefore, in this manuscript, we attempt to review the recently developed method and tried to analyze its implementation on natural convection in a staggered cavity with four differentially heated vertical walls. The problem geometry has eight boundaries. It is a staggered cavity with adiabatic horizontal walls and differentially heated vertical walls. The flow inside the thermally driven staggered cavity has been carefully studied for Rayleigh numbers 10³, 10⁴ and 10⁵. The velocity and pressure boundary conditions are determined by a non-equilibrium extrapolation rule. As no benchmark results are available in the literature for this relatively new problem, we carry out its simulation with the help of a yet another well established scheme. This scheme is a higher-order compact (HOC) scheme with fourth order spatial accuracy and second order temporal accuracy. Our results show that there is a very good agreement between both these methods which exemplifies the accuracy and credibility of our results.

• Periodical: Applied Mechanics and Materials (Volume 877)
• Pages: 366-371
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.877.366
• Online since: February 2018
• Authors: Bidyut B. Gogoi*
• Keywords: Differentially Heated, Heat Transfer, Higher-Order Compact, Lattice Boltzmann Method, Natural Convection, Rayleigh Numbers, Staggered Cavity

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