Develop lattice Boltzmann method and its related boundary conditions models for the benchmark oscillating walls by modif
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Develop lattice Boltzmann method and its related boundary conditions models for the benchmark oscillating walls by modifying hydrodynamic and thermal distribution functions Annunziata D’Orazio1, Arash Karimipour2,a , Amirhosein Mosavi3,4,b 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
Received: 28 September 2020 / Accepted: 5 November 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 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 D2 Q9 lattice. It is seen that the lid oscillation frequency effect is more significant at less amounts of Richardson number.
1 Introduction Various numerical approaches have been presented such as classic Navier–Stokes method or the particle base methods like molecular dynamic and lattice Boltzmann method (LBM). Using the classic methods for different flow regimes would need to some modifications through the solution process; however, the particle base methods could be basically applied for the macro-, micro- or even nanoscales flows. Meanwhile, LBM showed more suitable performance in some aspects of convergency, accuracy and the solution cost of time-consuming [1–4]. It led to report a large number of studies to examine the LBM ability at various conditions and geometries. However, the evaluation of LBM for the new more complicated problems can be estimated as the one of desired topics for researchers to increase this method usage [5–9]. Using LBM involves several advantages such as lack of difficulty for the multi-phase fluids such as nanofluids, in comparison with NS method, or there is no need to solve another
a e-mail: [email protected] b e-mail: [email protected] (corresponding author)
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equation for the pressure field. However, it should be mentioned that the solution process is more time-consuming for the macroscales levels [10–14]. On the other hand, LBM generally is a numerical approach to simulate the compressible ideal gases; it implies t
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