Eur. Phys. J. Plus (2020) 135: 915
https://doi.org/10.1140/epjp/s13360-020-00925-4

Regular Article

Develop lattice Boltzmann method and its related boundary conditions models for the benchmark oscillating walls by modifying hydrodynamic and thermal distribution functions

¹ Dipartimento di Ingegneria Astronautica, Elettrica ed Energetica, Sapienza Università di Roma, Via Eudossiana 18, 00184, Roma, Italy
² Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
³ Environmental Quality, Atmospheric Science and Climate Change Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam
⁴ Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam

^* e-mail: amirhosein.mosavi@tdtu.edu.vn

Received: 28 September 2020
Accepted: 5 November 2020
Published online: 17 November 2020

Abstract

Preset works aim to develop the lattice Boltzmann method ability to simulate the periodic supposed problems. Hence, a two-dimensional rectangular enclosure is considered so that its top cold lid oscillates horizontally with time. The stationary sidewalls are kept insulated. It would be necessary to present an appropriate boundary condition model of LBM for the oscillating lid, based on the hydrodynamic and thermal distribution functions. The influences of various lid oscillation frequencies (Strouhal number) are investigated at different values of Richardson numbers at free, mixed and force convections states by using D₂Q₉ lattice. It is seen that the lid oscillation frequency effect is more significant at less amounts of Richardson number.