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Computational Issues in the Simulation of Incompressible Flows Using the Lattice Boltzmann Method
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Abstract
The lattice Boltzmann (LB) method, which is closely related to the lattice Gas (LG) method, will be investigated in detail in this paper. The LG method is boolean in nature using only bits to indicate the presence or absence of a particle moving in a particular direction and speed. The absence of floating point operations gives the LG method unconditional numerical stability but restricts it to specialized hardware that can perform the Boolean logical operations efficiently. The Boolean character also results in a noisy signal that must be averaged over space/time for reliable estimates. The LB method, on the other hand, tracks the distribution functions (or time averages) of the particles. As a result, floating point numbers have to be used and so the method is not boolean. While this makes the LB method susceptible to instabilities due to accumulation of round-off errors, it allows the LB method to use a variety of existing computer platforms. The signal to noise ratio of the LB method is also significantly higher than the LG method. Both the LB method and the LG method are highly parallel. In fact, the LB method optimizes extremely well on current computer platforms as will be demonstrated in this paper. The current version of the LB code developed at FRL runs at speeds around 1.7 Gflops (2D code) and 2.0 Gflops (3D code) on a 32 processor Cray T3D. The 3D code has super-linear speedup (linear being the theoretical maximum) and runs at a speed of 33 Gflops on a 512 processor T3D. The objective of this paper is to demonstrate the potential of this method as a viable tool for performing time accurate simulations of incompressible flows. To that end, two issues will be examined in detail - accuracy and speed. The spatial and temporal accuracy of the LB method will be established through suitable benchmark studies. It is important to note here that the method is formally second order accurate in both space and time, an accuracy that exceeds that of many commercial codes today. The speed at which the code runs will be demonstrated through actual production runs on the parallel Cray T3D.
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Babu, V. and Strumolo, G., "Computational Issues in the Simulation of Incompressible Flows Using the Lattice Boltzmann Method," SAE Technical Paper 971519, 1997, https://doi.org/10.4271/971519.Also In
References
- McNamara G. Zanetti G. Physical Review Letters 61 2332 1988
- Chen S. Chen H. Martinez D. Matthaeus W. H. Physical Review Letters 67 3776 1991
- Qian Y. d'Humieres D. Lallemand P. Europhysics Letters 17 16 479 1992
- Bhatnagar P. L. Gross E. P. Krook M. Physics Review 94 511 1954
- Journal of Statistical Physics 81 1 2 October 1995
- Hou S. Zou Q. Chen S. Doolen G. Cogley A. C. Journal of Computational Physics 118 329 1995
- Ghia U. Ghia K. N. Shin C. T. Journal of Computational Physics 48 387 1982
- Hou S. “Lattice Boltzmann Method For Incompressible, Viscous Flow” Ph. D. Thesis Department of Mechanical Engineering, Kansas State University Manhattan, KS 1995
- He X. Luo L. S. “Lattice Boltzmann Model for the Incompressible Navier-Stokes Equation” 1995
- Zou Q. He X. “On Pressure and Velocity Flow Boundary Conditions for the Lattice Boltzmann BGK Model” Los Alamos e-print Archive 1995
- He X. Luo L.S. “A Priori Derivation of the Lattice Boltzmann Equation” Physical Review Letters 1996
- Armaly B. F. Durst F. Pereira J. C. F. Schonung B. Journal of Fluid Mechanics 127 473 1983
- Gartling D. K. International Journal For Numerical Methods In Fluids 11 953 1990
- Najm H. N. Ghoniem A. F. AIAA Journal 29 6 911 1991
- Schlichtung H. “Boundary Layer Theory” McGraw Hill Book Company New York, NY 1951
- Teixeira C. “Continuum Limit of Lattice Gas Fluid Dynamics” Ph. D. Thesis Department of Nuclear Engineering, Massachusetts Institute of Technology Cambridge, MA 1992