Application and Comparison of Different Lattice Boltzmann Methods on Non-Uniform Meshes for Simulation of Micro Cavity and Micro Channel Flow
Authors
Abstract
In this study, for the first time, a comparison of single-relaxation-time, multi-relaxation-time and entropic lattice Boltzmann methods on non-uniform meshes is performed and application of these methods for simulation of two-dimensional cavity flows, channel flows and channel flows with sudden expansion is studied in the slip and near transition regimes. In this work, Taylor series expansion and least squares based lattice Boltzmann method is utilized in order to apply the lattice Boltzmann models on non-uniform meshes. A diffuse scattering boundary condition and a combination of bounce-back and specular boundary conditions are employed to obtain the slip at the walls. Besides, the relaxation times of lattice Boltzmann methods are computed in terms of Knudsen number. Different lattice Boltzmann methods are used to simulate lid-driven micro cavity flows and their results are compared with each other and with those obtained in the literature. Then, the best model in accuracy and stability, i.e. multi-relaxation-time lattice Boltzmann method, is applied to simulate the micro channel flow in different Knudsen numbers. Results show that the proposed method on non-uniform meshes is capable of simulating micro flows problems in the slip and the transition regimes.
Keywords
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16. Ansumali, S., Karlin, I. V., Frouzakis, C. E., and Boulouchos, K. B., “Entropic Lattice Boltzmann Method for Microflows”, Physica A, Vol. 359, pp. 289-305, 2006.
17. Shirani, E., and Jafari, S., “Application of LBM in Simulation of Flow in Simple Micro-Geometries and Micro Porous Media”, African Physical Review, Vol. 1, No. 1, pp. 34-42, 2007.
18. Perumal, D. A., Krishna, V., Sarvesh, G., and Dass, A.K., “Numerical Simulation of Gaseous Microflows by Lattice Boltzmann Method”, International Journal of Recent Trends in Engineering, Vol. 1, No. 5, pp. 15-20, 2009.
19. Prasianakis, N., and Ansumali, S., “Microflow Simulations via the Lattice Boltzmann Method”, Communications in Computational Physics, Vol. 9, No. 5, pp. 1128-1136, 2011.
20. He, X., Luo, L. S., and Dembo, M., “Some Progress in Lattice Boltzmann Method, Part I. Non-Uniform Mesh Grids”, Journal of Computational Physics, Vol. 129, pp. 357-363, 1996.
21. Chew, Y. T., Shu, C., and Niu, X. D., “A New Differential Lattice Boltzmann Equation and Its Application to Simulate Incompressible Flows on Non-Uniform Grids”, Journal of Statistical Physics, Vol. 107, Nos. 1/2, pp. 329-342, 2002.
22. Fillipova, O., and Hänel, D., “Grid Refinement for Lattice-BGK Models”, Journal of Computational Physics, Vol. 147, pp. 219-228, 1998.
23. Fillipova O., and Hänel D., “Acceleration of Lattice-BGK Schemes with Grid Refinement”, Journal of Computational Physics., Vol. 165, pp. 407-427, 2000.
24. Shu C., Chew Y.T., and Niu X. D., “Least-Squares-Based Lattice Boltzmann Method: A Meshless Approach for Simulation of Flows with Complex Geometry”, Physical Review E, Vol. 64, No. 4, pp. 045701(1)-045701(4) , 2001.
25. Niu, X. D., Chew, Y. T., and Shu, C., “Simulation of Flows Around an Impulsively Started Circular Cylinder by Taylor Series Expansion and Least Squares-Based Lattice Boltzmann Method”, Journal of Computational Physics, Vol. 188, pp. 176-193, 2003.
26. Bhatnagar, P. L., Gross, E. P., and Krook, M., “A Model for Collision Process in Gases. l. Small Amplitude Processes in Charged and Neutral One-Component System”, Physical Review, Vol. 94, No. 3, pp. 511-525, 1954.
27. Mohamad, A. A., Lattice Boltzmann Method: Fundamentals and Engineering Applications with Computer Codes, Springer, 2011.
28. Ansumali, S., and Karlin, I. V., “Kinetic Boundary Condition for the Lattice Boltzmann Method”, Physical Review E, Vol. 66, No. 2, pp. 026311(1)-026311(6), 2002.
29. Chikatamarla, S. S., Ansumali, S., and Karlin, I. V., “Entropic Lattice Boltzmann Models for Hydrodynamics in Three Dimensions”, Physical Review Letters, Vol. 97, No. 1, pp. 010201(1)- 010201(4) , 2006.
30. Niu, X. D., Shu, C., and Chew Y. T., “Numerical Simulation of Isothermal Micro Flows by Lattice Boltzmann Method and Theoretical Analysis of the Diffuse Scattering Boundary Condition”, International Journal of Modern Physics C, Vol. 16, No. 12, pp. 1927–1941, 2005.
31. Mohammadzadeh, A., Roohi, E., and Niazmand, H., “A Parallel DSMC Investigation of Monatomic/Diatomic Gas Flows in a Micro/Nano Cavity”, Numerical Heat Transfer, Part A, Vol. 63, pp. 305–325, 2013.
32. Pong, K. C., Ho, C. M., Liu, J., and Tai, Y., “Non-Linear Pressure Distribution in Uniform Micro Channels”, In Application of Microfabrication to Fluid Mechanics, ASME Winter Annual Meeting, Vol. 197, pp. 51–56, 1994.
33. Knudsen, M., “Die Gesetze der Molecular Stromung und Dieinneren Reibungstromung der Gase Durch Rohren”, Annals of Physics, Vol. 28, pp. 75–130, 1909
34. Agrawal, A., Djenidi, L., and Antonia, R. A., “Simulation of Gas Flow in Microchannels with a Sudden Expansion or Contraction”, Journal of Fluid Mechanics, Vol. 530, pp. 135–144, 2005.
2. Wolf-Gladrow, D. A., Lattice-Gas Cellular Automata and Lattice Boltzmann Models - An Introduction, Springer Verlag, 2005.
1388.
4. He, X., Chen, S., and Doolen, D. G., “A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit”, Journal of Computational Physics, Vol. 146, pp. 282-300, 1998.
5. d’Humières, D., “Generalized Lattice Boltzmann Equations”, Rarefied Gas Dynamics: Theory and Simulations (Progress in Astronautics and Aeronautics), Vol. 159, pp. 450-458, 1994.
6. Ansumali, S., and Karlin, I. V., “Stabilization of the Lattice Boltzmann Method by the H Theorem: A Numerical Test”, Physical Review E, Vol. 62, No. 6, pp. 7999-8003, 2000.
7. Ansumali, S., and Karlin, I. V., “Single Relaxation Time Model for Entropic Lattice Boltzmann Methods”, Physical Review E, Vol. 65, No. 5, pp. 056312(1)- 056312(9) , 2002.
8. Rahmati, A. R., and Niazi, S., “Simulation of Microflows using the Lattice Boltzmann Method on Nonuniform Meshes”, International Journal of Nanomechanics Science and Technology, Vol. 3, No. 1, pp. 77-97, 2012.
10. Nie, X., Doolen, G. D., and Chen, S. Y., “Lattice-Boltzmann Simulations of Fluid Flows in MEMS”, Journal of Statistical Physics, Vol. 107, No. 1, pp. 279- 289, 2002.
11. Lim, C. Y., Shu, C., Niu, X. D., and Chew, Y. T., “Application of Lattice Boltzmann Method to Simulate Microchannel Flows”, Physics of Fluids, Vol. 14, No. 7, pp. 2299-2308, 2002.
12. Arkilic, E. B., Schmidt, M. A., and Breuer, K. S., “Gaseous Slip Flow in Long Microchannels”, Journal of Microelectromechanical Systems, Vol. 6, No. 2, pp. 167-178, 1997.
13. Niu, X. D., Shu, C., and Chew, Y. T., “A Lattice Boltzmann BGK Model for Simulation of Micro Flows”, Europhysics Letters, Vol. 67, No. 4, pp. 600-606, 2004.
14. Tang, G. H., Tao, W. Q., and He, Y. L., “Lattice Boltzmann Method for Gaseous Microflows using Kinetic Theory Boundary Conditions”, Physics of Fluids, Vol. 17, No. 5, pp. 058101(1)-058101(4) , 2005.
15. Zhang, Y. H., Qin, R. S., Sun, Y. H., Barber, R. W., and Emerson, D. R., “Gas Flow in Microchannel- A Lattice Boltzmann Method Approach”, Journal of Statistical Physics, Vol. 121, No. 1, pp. 257-267, 2005.
16. Ansumali, S., Karlin, I. V., Frouzakis, C. E., and Boulouchos, K. B., “Entropic Lattice Boltzmann Method for Microflows”, Physica A, Vol. 359, pp. 289-305, 2006.
17. Shirani, E., and Jafari, S., “Application of LBM in Simulation of Flow in Simple Micro-Geometries and Micro Porous Media”, African Physical Review, Vol. 1, No. 1, pp. 34-42, 2007.
18. Perumal, D. A., Krishna, V., Sarvesh, G., and Dass, A.K., “Numerical Simulation of Gaseous Microflows by Lattice Boltzmann Method”, International Journal of Recent Trends in Engineering, Vol. 1, No. 5, pp. 15-20, 2009.
19. Prasianakis, N., and Ansumali, S., “Microflow Simulations via the Lattice Boltzmann Method”, Communications in Computational Physics, Vol. 9, No. 5, pp. 1128-1136, 2011.
20. He, X., Luo, L. S., and Dembo, M., “Some Progress in Lattice Boltzmann Method, Part I. Non-Uniform Mesh Grids”, Journal of Computational Physics, Vol. 129, pp. 357-363, 1996.
21. Chew, Y. T., Shu, C., and Niu, X. D., “A New Differential Lattice Boltzmann Equation and Its Application to Simulate Incompressible Flows on Non-Uniform Grids”, Journal of Statistical Physics, Vol. 107, Nos. 1/2, pp. 329-342, 2002.
22. Fillipova, O., and Hänel, D., “Grid Refinement for Lattice-BGK Models”, Journal of Computational Physics, Vol. 147, pp. 219-228, 1998.
23. Fillipova O., and Hänel D., “Acceleration of Lattice-BGK Schemes with Grid Refinement”, Journal of Computational Physics., Vol. 165, pp. 407-427, 2000.
24. Shu C., Chew Y.T., and Niu X. D., “Least-Squares-Based Lattice Boltzmann Method: A Meshless Approach for Simulation of Flows with Complex Geometry”, Physical Review E, Vol. 64, No. 4, pp. 045701(1)-045701(4) , 2001.
25. Niu, X. D., Chew, Y. T., and Shu, C., “Simulation of Flows Around an Impulsively Started Circular Cylinder by Taylor Series Expansion and Least Squares-Based Lattice Boltzmann Method”, Journal of Computational Physics, Vol. 188, pp. 176-193, 2003.
26. Bhatnagar, P. L., Gross, E. P., and Krook, M., “A Model for Collision Process in Gases. l. Small Amplitude Processes in Charged and Neutral One-Component System”, Physical Review, Vol. 94, No. 3, pp. 511-525, 1954.
27. Mohamad, A. A., Lattice Boltzmann Method: Fundamentals and Engineering Applications with Computer Codes, Springer, 2011.
28. Ansumali, S., and Karlin, I. V., “Kinetic Boundary Condition for the Lattice Boltzmann Method”, Physical Review E, Vol. 66, No. 2, pp. 026311(1)-026311(6), 2002.
29. Chikatamarla, S. S., Ansumali, S., and Karlin, I. V., “Entropic Lattice Boltzmann Models for Hydrodynamics in Three Dimensions”, Physical Review Letters, Vol. 97, No. 1, pp. 010201(1)- 010201(4) , 2006.
30. Niu, X. D., Shu, C., and Chew Y. T., “Numerical Simulation of Isothermal Micro Flows by Lattice Boltzmann Method and Theoretical Analysis of the Diffuse Scattering Boundary Condition”, International Journal of Modern Physics C, Vol. 16, No. 12, pp. 1927–1941, 2005.
31. Mohammadzadeh, A., Roohi, E., and Niazmand, H., “A Parallel DSMC Investigation of Monatomic/Diatomic Gas Flows in a Micro/Nano Cavity”, Numerical Heat Transfer, Part A, Vol. 63, pp. 305–325, 2013.
32. Pong, K. C., Ho, C. M., Liu, J., and Tai, Y., “Non-Linear Pressure Distribution in Uniform Micro Channels”, In Application of Microfabrication to Fluid Mechanics, ASME Winter Annual Meeting, Vol. 197, pp. 51–56, 1994.
33. Knudsen, M., “Die Gesetze der Molecular Stromung und Dieinneren Reibungstromung der Gase Durch Rohren”, Annals of Physics, Vol. 28, pp. 75–130, 1909
34. Agrawal, A., Djenidi, L., and Antonia, R. A., “Simulation of Gas Flow in Microchannels with a Sudden Expansion or Contraction”, Journal of Fluid Mechanics, Vol. 530, pp. 135–144, 2005.
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