Hostname: page-component-8448b6f56d-wq2xx Total loading time: 0 Render date: 2024-04-25T05:39:29.168Z Has data issue: false hasContentIssue false

Lattice Boltzmann Simulations of Cavity Flows on Graphic Processing Unit with Memory Management

Published online by Cambridge University Press:  04 September 2017

P. Y. Hong
Affiliation:
Department of Power Mechanical EngineeringNational Tsing Hua UniversityHsinchu, Taiwan
L. M. Huang
Affiliation:
Department of Power Mechanical EngineeringNational Tsing Hua UniversityHsinchu, Taiwan
C. Y. Chang
Affiliation:
Department of Power Mechanical EngineeringNational Tsing Hua UniversityHsinchu, Taiwan
C. A. Lin*
Affiliation:
Department of Power Mechanical EngineeringNational Tsing Hua UniversityHsinchu, Taiwan
*
*Corresponding author (calin@pme.nthu.edu.tw)
Get access

Abstract

Lattice Boltzmann method (LBM) is adopted to compute two and three-dimensional lid driven cavity flows to examine the influence of memory management on the computational performance using Graphics Processing Unit (GPU). Both single and multi-relaxation time LBM are adopted. The computations are conducted on nVIDIA GeForce Titan, Tesla C2050 and GeForce GTX 560Ti. The performance using global memory deteriorates greatly when multi relaxation time (MRT) LBM is used, which is due to the scheme requesting more information from the global memory than its single relaxation time (SRT) LBM counterpart. On the other hand, adopting on chip memory the difference using MRT and SRT is not significant. Also, performance of LBM streaming procedure using offset reading surpasses offset writing ranging from 50% to 100% and this applies to both SRT and MRT LBM. Finally, comparisons using different GPU platforms indicate that Titan as expected outperforms other devices, and attains 227 and 193 speedup over its Intel Core i7-990 CPU counterpart and four times faster than GTX 560Ti and Tesla C2050 for three dimensional cavity flow simulations respectively with single and double precisions.

Type
Research Article
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Shankar, P. N. and Deshpande, M. D., “Fluid Mechanics in the Driven Cavity,” Annual Review of Fluid Mechanics, 32, 93 (2000).Google Scholar
2. Ghia, U., Ghia, K. N. and Shin, C. T., “High-Resolutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method,” Journal of Computational Physics, 48, 387 (1982).Google Scholar
3. Schreiber, R. and Keller, H. B., “Driven Cavity Flows by Effcient Numerical Techniques,” Journal of Computational Physics, 49, 310 (1983).Google Scholar
4. Iwatsu, R., Ishii, K., Kawamura, T., Kuwahara, K. and Hyun, J. M., “Numerical Simulation of Three-Dimensional Flow Structure in a Driven Cavity,” Fluid Dynamics Research, 5, 173 (1989).CrossRefGoogle Scholar
5. Guj, G. and Stella, F., “A Vorticity-Velocity Method for the Numerical Solution of 3D Incompressible Flows,” Journal of Computational Physics, 106, 286 (1993).Google Scholar
6. Mei, R., Shyy, W., Yu, D. and Luo, L. S., “Lattice Boltzmann Method for 3-D Flows with Curved Boundary,” Journal of Computational Physics, 161, 680 (2000).Google Scholar
7. Feldman, Y. and Gelfgat, A. Y., “Oscillatory Instability of a Three-Dimensional Lid-Driven Flow in a Cube,” Physics of Fluids, 22, 093602 (2010).Google Scholar
8. Liberzon, A., Feldman, Y. and Gelfgat, A. Y., “Experimental Observation of the Steady-Oscillatory Transition in a Cubic Lid-Driven Cavity,” Physics of Fluids, 23, 084106 (2011).Google Scholar
9. Hou, S., Zou, Q., Chen, S., Doolean, G. and Cogley, A. C., “Simulation of Cavity Flow by the Lattice Boltzmann Method,” Journal of Computational Physics, 118, 329 (1995).Google Scholar
10. Lin, L. S., Chen, Y. C. and Lin, C. A., “Multi Relaxation Time Lattice Boltzmann Simulations of Deep Lid Driven Cavity Flows at Different Aspect Ratios,” Computers & Fluids, 45, 233 (2011).Google Scholar
11. Ghadyani, M. and Esfahanian, V., “A More Robust Compressible Lattice Boltzmann Model by Using the Numerical Filters,” Journal of Mechanics, 30, 515 (2014).Google Scholar
12. Lin, S. Y. et al., “A Unified Wall-Boundary Condition for the Lattice Boltzmann Method and Its Application to Force Evaluation,” Journal of Mechanics, 31, 55 (2015).Google Scholar
13. Cuda C Programming Guide 5.0, http://developer.nvidia.com/cuda-gpus (2012)Google Scholar
14. Obrecht, C., Kuznik, F., Tourancheau, B. and Roux, J. J., “A New Approach to the Lattice Boltzmann Method for Graphics Processing Units,” Computers and Mathematics with Applications, 61, 3628 (2011).Google Scholar
15. Kuznik, F., Obrecht, C., Rusaouen, G. and Roux, J. J., “LBM Based Flow Simulation Using GPU Computing Processor,” Computers and Mathematics with Applications, 59, 2380 (2010).Google Scholar
16. Tölke, J., “Implementation of a Lattice Boltzmann Kernel Using the Compute Unified Device Architecture Developed by nVIDIA,” Computing and Visualization in Science, 13, 29 (2010).Google Scholar
17. Lin, L. S., Chang, H. W. and Lin, C. A., “Multi Relaxation Time Lattice Boltzmann Simulations of Transition in Deep 2D Lid Driven Cavity Using GPU,” Computers & Fluids, 80, 381 (2013).Google Scholar
18. Chang, H. W., Hong, P. Y., Lin, L. S. and Lin, C. A., “Simulations of Flow Instability in Three Dimensional Deep Cavities with Multi Relaxation Time Lattice Boltzmann Method on Graphic Processing Units,” Computers & Fluids, 88, 866 (2013).Google Scholar
19. Hong, P. Y., Huang, L. M., Lin, L. S. and Lin, C. A., “Scalable Multi-Relaxation-Time Lattice Boltzmann Simulations on Multi-GPU Cluster,” Computers & Fluids, 110, 1 (2015).Google Scholar
20. Qian, Y. H., d'Humières, D. and Lallemand, P., “Lattice BGK Models for Navier-Stokes Equation,” Europhys Lett, 17, 479 (1992).Google Scholar
21. Humières, D., Ginzburg, I., Krafczyk, M., Lallemand, P. and Luo, L. S., “Multiple-Relaxation-Time Lattice Boltzmann Models in Three Dimensions,” Philosophical Transactions of the Royal Society of London A, 360, 437 (2002).Google Scholar
22. Lallemand, P. and Luo, L. S., “Theory of the Lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability,” Physical Review E, 61, 6546 (2000).Google Scholar
23. Ho, C. F., Chang, C., Lin, K. H. and Lin, C. A., “Consistent Boundary Conditions for 2D and 3D Laminar Lattice Boltzmann Simulations,” CMES-Computer Modeling in Engineering and Sciences, 44, 137 (2009).Google Scholar
24. Chang, C., Liu, C. H. and Lin, C. A., “Boundary Conditions for Lattice Boltzmann Simulations with Complex Geometry Flows,” Computers and Mathematics with applications, 58, 940 (2009).CrossRefGoogle Scholar
25. Albensoeder, S. and Kuhlmann, H. C., “Accurate Three-Dimensional Lid-Driven Cavity Flow,” Journal of Computational Physics, 206, 536 (2005).Google Scholar