Investigation of the influence of the relaxation parameter on the viscous fluid flow over circular cylinder modeling process with the lattice Boltzmann method
Keywords:
relaxation parameter, lattice, Boltzmann equation, numerical solution
Abstract
In this work we investigate the influence of the relaxation parameter for the lattice Boltzmann method on the flow modeling process for the viscous fluid. The relaxation parameter influence on the other method parameters, the simulation time and the numerical solution stability has been considered by example of the fluid flow around circular cylinder modeling in a plane channel. Modeling has been performed at moderate Reynolds numbers. The flow pattern, the drag coefficient of the cylinder and the calculation time for the different Reynolds numbers have been shown. The results have been compared with the known experimental data and the other numerical solutions.Downloads
Download data is not yet available.
References
Succi S. The Lattice Boltzmann Equation: A New Tool For Computational Fluid-Dynamics // Physica D: Nonlinear Phenomena. – 1991. – Vol. 47. – P. 219-230.
Strang G. An Analysis of The Finite Element Method. – Englewood-Cliffs: Prentice Hall, 1973. – 400 p.
Ogami Y. Viscous flow simulation using the discrete vortex model - the diffusion velocity method // Computers & Fluids. – 1991. – 19(3). – P. 433-441.
Martinez D.O., Matthaeus W.H, Chen S., Montgomery D.C. Comparison of spectral method and lattice Boltzmann simulations of two-dimensional hydrodynamics // Phys. Fluids. – 1994. – 6(3). – P.1285-1298.
Leclaire S., Pellerin N., Reggio M., Trepanier J.-Y. Enhanced equilibrium distribution functions for simulating immiscible multiphase flows with variable density ratios in a class of lattice Boltzmann models // International Journal of Multiphase Flow. – 2003. – 57. – P. 159-168.
Li Q., Luo K.H., Kang Q.J., Chen Q., Liu Q. Lattice Boltzmann method for multiphase flow and phase-change heat transfer // Progress in Energy and Combustion Science. – 2016. – 52. – P. 62–105.
Favier J. Revell A., Pinelli A. A lattice Boltzmann-immersed boundary method to simulate the fluid interaction with moving and slender flexible objects // Journal of Computational Physics. – 2014. – № 261. – P. 145-161.
Grazyna K. The numerical solution of the transient heat conduction problem using the lattice Boltzmann method // Scientific Research of the Institute of Mathematics and Computer Science. – 2006. – № 11. – P. 23-30.
Favier J., Revell A., Pinelli A. A lattice Boltzmann-immersed boundary method to simulate the fluid interaction with moving and slender flexible objects // Journal of Computational Physics. – 2014. – № 261. – P. 145-161.
R. Mei, D. Yu, W. Shyy, L. Luo Force evaluation in the lattice Boltzmann method involving curved geometry// Physical review. – 2002. – Vol.65. – P. 65-78.
Peruman D. A., Kumar V.S., Dass A.K. Lattice Boltzmann simulation over a circular cylinder at moderate Reynolds numbers // Thermal Science. – 2014. – V.18, № 4. – P. 1235-1246
Peruman D. A., Kumar V.S., Dass A.K. Numerical Simulation of Viscous Flow over a Square Cylinder Using Lattice Boltzmann Method // Mathematical Physics. – 2012. – Vol. 12. – P. 1-16.
Бикулов Д.А., Сенин Д.С., Демин Д.С., Дмитриев А.В., Грачев Н.Е. Реализация метода решеточных уравнений Больцмана для расчетов на GPU-кластере // Вычислительные методы и программирование. – 2012. – Т.13. – С.13-19.
Wolf-Gladrow D. Lattice-Gas Cellular Automata and Lattice Boltzmann Models - An Introduction. – Bremerhaven: Alfred Wegener Institute for Polar and Marine, 2005. – 311 p.
Sucop M. Lattice Boltzmann Modeling. An Introduction for Geoscientists and Engineers. – Miami: Springer, 2006. – 177 p.
Кривовичев Г.В. О применении интегро-интерполяционного метода к построению одношаговых решеточных кинетических схем Больцмана // Вычислительные методы и программирование. – 2012. – Т.13. – С.19-27.
Rettinger C. Fluid Flow Simulation using the Lattice Boltzmann Method with multiple relaxation times. – Erlanger-Nuremberg: Friedrich-Alexander University, 2013. – 38 p.
Mussa M. Numerical Simulation of Lid-Driven Cavity Flow Using the Lattice Boltzmann Method // Applied Mathematics. – 2008. – Vol. 13. – P. 236-240.
Nemati H., Farhadi M., Sedighi K., Fattahi E. Multi-Relaxation-Time Lattice Boltzmann Model For Uniform-Shear Flow Over a Rotating Circular Cylinder // Thermal Science. – 2011. – Vol. 15, No. 3. – P. 859-878.
Reunsumrit J. The Lattice Boltzmann Method for Investigating the Fluid Flow Pattern in 2D Channel through Triangle Obstacle // Applied Mathematical Sciences. – 2013. – Vol.7, no. 65. – P. 3215-3223.
Куперштох А.Л. Трехмерное моделирование двухфазных систем типа жидкость-пар методом решеточных уравнений Больцмана на GPU // Вычислительные методы и программирование. – 2012. – Т.13. – С.130-138.
Ляпин И.И. Введение в теорию кинетических уравнений: Учебное пособие. – Екатеринбург: УГТУ-УПИ, 2003. – 205 с.
Куперштох А.Л. Метод решеточных уравнений Больцмана для моделирования двухфазных систем типа жидкость-пар // Современная наука. – 2010. – №2(4). – С. 56-63.
He X. Lattice Boltzmann Model for the Incompressible Navier – Stokes Equation // Journal of statistical physics. – 1997. – Vol.88. – P. 927–944.
Bulanchuk G., Bulanchuk O., Ostapenko A. Stability investigation of the two-dimensional nine-vectors model of the lattice Boltzmann method for fluid flows in a square cavity // Вестник Харьковского нац. унив. им. В.Н. Каразина. Серия: Математическое моделирование. Информационные технологии. Автоматизированные системы управления. – 2015. – № 28. – С. 113-125.
Tritton D.J. Experiments on the Flow Past a Circular Cylinder at Low Reynolds Numbers // Journal of Fluid Mechanics. – 1959. – 6(4). – P. 547-555.
Calhoun D. A Cartesian grid Method for Solving the Two-Dimentional Streamfunction-Vorticity Equations in Irregular Regions // Journal of Computational Physics. – 2002. – 176. – P. 231-275.
Strang G. An Analysis of The Finite Element Method. – Englewood-Cliffs: Prentice Hall, 1973. – 400 p.
Ogami Y. Viscous flow simulation using the discrete vortex model - the diffusion velocity method // Computers & Fluids. – 1991. – 19(3). – P. 433-441.
Martinez D.O., Matthaeus W.H, Chen S., Montgomery D.C. Comparison of spectral method and lattice Boltzmann simulations of two-dimensional hydrodynamics // Phys. Fluids. – 1994. – 6(3). – P.1285-1298.
Leclaire S., Pellerin N., Reggio M., Trepanier J.-Y. Enhanced equilibrium distribution functions for simulating immiscible multiphase flows with variable density ratios in a class of lattice Boltzmann models // International Journal of Multiphase Flow. – 2003. – 57. – P. 159-168.
Li Q., Luo K.H., Kang Q.J., Chen Q., Liu Q. Lattice Boltzmann method for multiphase flow and phase-change heat transfer // Progress in Energy and Combustion Science. – 2016. – 52. – P. 62–105.
Favier J. Revell A., Pinelli A. A lattice Boltzmann-immersed boundary method to simulate the fluid interaction with moving and slender flexible objects // Journal of Computational Physics. – 2014. – № 261. – P. 145-161.
Grazyna K. The numerical solution of the transient heat conduction problem using the lattice Boltzmann method // Scientific Research of the Institute of Mathematics and Computer Science. – 2006. – № 11. – P. 23-30.
Favier J., Revell A., Pinelli A. A lattice Boltzmann-immersed boundary method to simulate the fluid interaction with moving and slender flexible objects // Journal of Computational Physics. – 2014. – № 261. – P. 145-161.
R. Mei, D. Yu, W. Shyy, L. Luo Force evaluation in the lattice Boltzmann method involving curved geometry// Physical review. – 2002. – Vol.65. – P. 65-78.
Peruman D. A., Kumar V.S., Dass A.K. Lattice Boltzmann simulation over a circular cylinder at moderate Reynolds numbers // Thermal Science. – 2014. – V.18, № 4. – P. 1235-1246
Peruman D. A., Kumar V.S., Dass A.K. Numerical Simulation of Viscous Flow over a Square Cylinder Using Lattice Boltzmann Method // Mathematical Physics. – 2012. – Vol. 12. – P. 1-16.
Бикулов Д.А., Сенин Д.С., Демин Д.С., Дмитриев А.В., Грачев Н.Е. Реализация метода решеточных уравнений Больцмана для расчетов на GPU-кластере // Вычислительные методы и программирование. – 2012. – Т.13. – С.13-19.
Wolf-Gladrow D. Lattice-Gas Cellular Automata and Lattice Boltzmann Models - An Introduction. – Bremerhaven: Alfred Wegener Institute for Polar and Marine, 2005. – 311 p.
Sucop M. Lattice Boltzmann Modeling. An Introduction for Geoscientists and Engineers. – Miami: Springer, 2006. – 177 p.
Кривовичев Г.В. О применении интегро-интерполяционного метода к построению одношаговых решеточных кинетических схем Больцмана // Вычислительные методы и программирование. – 2012. – Т.13. – С.19-27.
Rettinger C. Fluid Flow Simulation using the Lattice Boltzmann Method with multiple relaxation times. – Erlanger-Nuremberg: Friedrich-Alexander University, 2013. – 38 p.
Mussa M. Numerical Simulation of Lid-Driven Cavity Flow Using the Lattice Boltzmann Method // Applied Mathematics. – 2008. – Vol. 13. – P. 236-240.
Nemati H., Farhadi M., Sedighi K., Fattahi E. Multi-Relaxation-Time Lattice Boltzmann Model For Uniform-Shear Flow Over a Rotating Circular Cylinder // Thermal Science. – 2011. – Vol. 15, No. 3. – P. 859-878.
Reunsumrit J. The Lattice Boltzmann Method for Investigating the Fluid Flow Pattern in 2D Channel through Triangle Obstacle // Applied Mathematical Sciences. – 2013. – Vol.7, no. 65. – P. 3215-3223.
Куперштох А.Л. Трехмерное моделирование двухфазных систем типа жидкость-пар методом решеточных уравнений Больцмана на GPU // Вычислительные методы и программирование. – 2012. – Т.13. – С.130-138.
Ляпин И.И. Введение в теорию кинетических уравнений: Учебное пособие. – Екатеринбург: УГТУ-УПИ, 2003. – 205 с.
Куперштох А.Л. Метод решеточных уравнений Больцмана для моделирования двухфазных систем типа жидкость-пар // Современная наука. – 2010. – №2(4). – С. 56-63.
He X. Lattice Boltzmann Model for the Incompressible Navier – Stokes Equation // Journal of statistical physics. – 1997. – Vol.88. – P. 927–944.
Bulanchuk G., Bulanchuk O., Ostapenko A. Stability investigation of the two-dimensional nine-vectors model of the lattice Boltzmann method for fluid flows in a square cavity // Вестник Харьковского нац. унив. им. В.Н. Каразина. Серия: Математическое моделирование. Информационные технологии. Автоматизированные системы управления. – 2015. – № 28. – С. 113-125.
Tritton D.J. Experiments on the Flow Past a Circular Cylinder at Low Reynolds Numbers // Journal of Fluid Mechanics. – 1959. – 6(4). – P. 547-555.
Calhoun D. A Cartesian grid Method for Solving the Two-Dimentional Streamfunction-Vorticity Equations in Irregular Regions // Journal of Computational Physics. – 2002. – 176. – P. 231-275.
Published
2017-05-29
How to Cite
Bulanchuk, G. G., & Ostapenko, A. A. (2017). Investigation of the influence of the relaxation parameter on the viscous fluid flow over circular cylinder modeling process with the lattice Boltzmann method. Bulletin of V.N. Karazin Kharkiv National University, Series «Mathematical Modeling. Information Technology. Automated Control Systems», 33, 52-61. Retrieved from https://periodicals.karazin.ua/mia/article/view/9187
Issue
Section
Статті
