Stability investigation of the two-dimensional nine-vectors model of the lattice Boltzmann method for fluid flows in a square cavity
Анотація
In this paper we consider the stability of the two-dimensional nine-vectors model of the lattice Boltzmann method which used to model fluid flows in a square lid-driven cavity. Obtained numerical solutions were compared with the results of the numerical experiments by the finite element method. We investigate the influence of Reynolds and Mach numbers on method`s stability. Shown the dependence between the kinematic viscosity of the modeling liquid and cell`s size. Have been shown the advantages and disadvantages of this computational method.Завантаження
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Посилання
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14. Г. В. Кривовичев О расчете течений вязкой жидкости методом решеточных уравнений Больцмана// Компьютерные исследования и моделирование. – 2013. – Т.5 №2. – 165-178 стр.
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17. M. Sucop Lattice Boltzmann Modeling. An Introduction for Geoscientists and Engineers. – Miami, 2006. – 171 p
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2. G. Strang An Analysis of The Finite Element Method. Prentice Hall. – Prentice Hall, 1973. – 400 p.
3. R. Eymard, T.R. Gallouet, R. Herbin The finite volume method Handbook of Numerical Analysis. – Paris, 2000. – 1020 p.
4. Белоцерковский С. М., Скобелев Б. Ю. Метод дискретных вихрей и турбулентность. – Новосибирск: ИТПМ, 1993. — 38 с.
5. Y. Ogami, T. Akamatsu Viscous flow simulation using the discrete vortex model -the diffusion velocity method // Computers & Fluids. — 1991. — Vol. 19, no. 3/4. — 433-441 p.
6. J.J. Monaghan An introduction to SPH// Computer Physics Communications. – 1988. – vol. 48. – pp. 88-96.
7. A. J. Chorin Numerical Solution of the Navier-Stokes Equations// Mathematics of Computation. – 1968. – Vol.22, No.104. – 745-762 p.
8. D. O. Martinez, W. H. Matthaeus, S. Chen, D.C. Montgomery Comparison of spectral method and lattice Boltzmann simulations of two-dimentional hydrodynamics// Physics of Fluids. – 1994. – Vol.6, No 3. – P. 1285-1298
9. Белоцерковский О.М. Численное моделирование в механике сплошных сред. – М.: Наука, 1984. – 520 с.
10. L. S. Luo Theory of the lattice Boltzmann method: lattice Boltzmann models for nonideal gases// Physical Rexiew. – 2000. – Vol.62, No 4. – P. 4292-4996
11. S. Succi The lattice Boltzmann equation: a new tool for computational fluid dynamics//Physica D. – 1991. – V.47 №. 1. – 219–230 p.
12. С. Rettinger Fluid Flow Simulation using the Lattice Boltzmann Method with multiple relaxation times. – Bachelor, 2013. – 38 p.
13. M. Mussa Numerical Simulation of Lid – Driven Cavity Flow Using the Lattice Boltzmann Method// Applied Mathematics. – 2008. – 236-240 p.
14. Г. В. Кривовичев О расчете течений вязкой жидкости методом решеточных уравнений Больцмана// Компьютерные исследования и моделирование. – 2013. – Т.5 №2. – 165-178 стр.
15. M. Van Dyke An Album of Fluid Motion. – California: The Parabolic Press, 1982. – 184 p
16. S. Succi The Lattice Boltzmann Equation for Fluid Dinamics and Beyond. – Oxford: Univercity Press, 2001. – 288 p
17. M. Sucop Lattice Boltzmann Modeling. An Introduction for Geoscientists and Engineers. – Miami, 2006. – 171 p
18. D. Wolf-Gladrow Lattice-Gas Cellular Automata and Lattice Boltzmann Models - An Introduction . – Bremerhaven: Alfred Wegener Institute for Polar and Marine, 2005. – 273 p
19. X. He Lattice Boltzmann Model for the Incompressible Navier – Stokes Equation//Journal of statistical physics. – 1997. – V.88. – 927–944 p.
Опубліковано
2015-11-30
Як цитувати
Bulanchuk, G., Bulanchuk, O., & Ostapenko, A. (2015). Stability investigation of the two-dimensional nine-vectors model of the lattice Boltzmann method for fluid flows in a square cavity. Вісник Харківського національного університету імені В.Н. Каразіна, серія «Математичне моделювання. Інформаційні технології. Автоматизовані системи управління», 28, 113-125. вилучено із https://periodicals.karazin.ua/mia/article/view/5477
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