Lid-Driven Cavity For Mantle Convection Modelling Using Lattice Boltzmann Method
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Abstract
The Lattice Boltzmann Method is one of the computational fluid dynamics methods that can be applied to simulate fluid based on the microscopic and kinetic theory of gases. In this study, earth mantle convection is simulated by combining the concept of lid-driven cavity simulation and natural convection using the Lattice Boltzmann method in a two-dimensional system (D2Q9). The results of the lid-driven cavity and natural convection simulation are comparable to previous works. This study shows that at a certain lid velocity, the direction of the moving plume is changed. This earth mantle convection simulation will give better and more reliable results by considering more complicated boundary conditions and adequate simulation systems.
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Fauzi, umar. (2021). Lid-Driven Cavity For Mantle Convection Modelling Using Lattice Boltzmann Method. Indonesian Journal of Physics, 32(1), 21-28. https://doi.org/10.5614/itb.ijp.2021.32.1.3
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References
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[15] Renkun Dai, Qingfei Bian, Qiuwang Wang, Min Zeng, Evolution of natural convection melting inside cavity heated from different sides using enthalpy based lattice Boltzmann method, International Journal of Heat and Mass Transfer 121, 715–725, 2018.
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[3] Frisch, U; d'Humieres, D; Hasslacher, B; Lal-lemand, P; Pomeau, Y; Rivet, J P. Lattice gas hydrodynamics in two and three dimensions. Conference: Modern approaches to large non-linear physical systems workshop, Santa Fe, NM, USA, 27 Oct 1986.
[4] Daniel H. Rothman, Stiphane Zaleski, Lattice-Gas Cellular Automata: Simple Models of Complex Hydrodynamics, Cambridge Univer-sity Press, 1997.
[5] Mohamad, A. A.. Lattice Boltzmann Method: Fundamentals and Engineering Applications with Computer Codes. London: Springer., 2011
[6] He, X., & Luo, L. S.. Theory of the lattice Boltzmann method: From the Boltzmann equa-tion to the lattice Boltzmann equation. Physi-cal Review E, 6811-6817, 1997.
[7] Wolf-Gladrow, D. A.. Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction. Germany: Springer, 2000.
[8] Guy R. McNamara and Gianluigi Zanetti, Use of the Boltzmann Equation to Simulate Lattice-Gas Automata, Phys. Rev. Lett. 61, 2332, 1988.
[9] F. J. Higuera1 and J. Jiménez, Boltzmann Ap-proach to Lattice Gas Simulations EPL (Euro-physics Letters), Volume 9, Number 7, EPL 9 663, 1989.
[10] Bhatnagar, P. L., Gross, E. P., & Krook, M.. A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems. Physical Review, 511-525, 1954.
[11] James D. Sterling and ShiyiChen, Stability Analysis of Lattice Boltzmann Methods, Jour-nal of Computational Physics Volume 123, Is-sue 1, Pages 196-206, 1996
[12] Zhaoli Guo and T. S. Zhao, A Lattice Boltz-mann Model For Convection Heat Transfer In Porous Media, Numerical Heat Transfer, Part B, 47: 157–177, 2005.
[13] Jia Wanga, Donghai Wanga, Pierre Lallemand b, Li-Shi Luo, Lattice Boltzmann simulations of thermal convective flows in two dimen-sions, Computers and Mathematics with Ap-plications 65, 262–286, 2013.
[14] Peter Mora and David A. Yuen, Simulation of plume dynamics by the Lattice Boltzmann Method, Geophys. J. Int., 210, 1932–1937, 2017.
[15] Renkun Dai, Qingfei Bian, Qiuwang Wang, Min Zeng, Evolution of natural convection melting inside cavity heated from different sides using enthalpy based lattice Boltzmann method, International Journal of Heat and Mass Transfer 121, 715–725, 2018.
[16] Ziliang Rui, Juan Li, Jie Ma, Han Cai, Binjian Nie, Hao Peng, Comparative study on natural convection melting in the square cavity using lattice Boltzmann method, Results in Physics 18,103274, 2020.
[17] Abderrahmane Bourada, Asma Ouahouah, Kaoutar Bouarnouna, Karim Ragui1, Abdelka-der Boutra1, 2, and Youb Khaled Benkahla1, Multiple-relaxation-time Lattice Boltzmann model for flow and convective heat transfer in lid-driven cavity with a porous obstacle, MATEC Web of Conferences 330, 01007, 2020.
[18] Becker, T. W., Global plate kinematics and dynamical models of the mantle, American Geophysical Union, Fall Meeting 2018.
[19] Ghia, U., Ghia, K. N., & Shin, C. T. (1982). High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Mul-tigrid Method. Journal of Computational Phys-ics, 387-411.
[20] Chandrasekhar, S. (1961). Hydrodynamic and Hydromagnetic Stability. London: Oxford Uni-versity Press.