THERMAL SCIENCE

International Scientific Journal

LATTICE BOLTZMANN METHOD AND DIFFUSION IN MATERIALS WITH LARGE DIFFUSIVITY RATIOS

ABSTRACT
This work is centered on the safe usage of the lattice Boltzmann method for 2-D pure diffusion. The basics of the method for pure diffusion are first elucidated using a new definition given in the paper. The oscillating behavior and safe conditions of use are then explored in the case of homogeneous material as well as heterogeneous materials with circular and plane interfaces. As a conclusion, the range of valid relaxation factors is given for a correct use of lattice Boltzmann method.
KEYWORDS
PAPER SUBMITTED: 2014-10-27
PAPER REVISED: 2016-04-30
PAPER ACCEPTED: 2016-06-21
PUBLISHED ONLINE: 2016-09-05
DOI REFERENCE: https://doi.org/10.2298/TSCI141027206W
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE 3, PAGES [1173 - 1182]
REFERENCES
  1. Mohamad A.A., Lattice Boltzmann Method - Fundamentals and Engineering Applications with Computer Codes, Springer Edition, 2011.
  2. Walther, E., Bogdan, M., Bennacer, R., De Sa, C. Cement paste morphologies and effective diffusivity: using the Lattice Boltzmann method. European Journal of Environmental and Civil Engineering, 19, (2015), 10, pp. 1-13.
  3. Ganaoui, M. El., Semma, E. A. A Lattice Boltzmann Coupled to Finite Volumes Method for Solving Phase Change Problems. Thermal Science, 13, (2009), 2, pp. 205-216.
  4. Jourabian, M., Farhadi, M., Rabienataj Darzi, A.-A., Abouei, A. Lattice Boltzmann simulation of melting phenomenon with natural convection from an excentric annulus. Thermal Science, 17, (2013), 3, pp. 877-890.
  5. Wolf-Gladrow D.A., Lattice-Gas Cellular automata and Lattice Boltzmann Models - An Introduction, Springer, 2000.
  6. Servan-Camas B., Tsai F.-T.-C. Non-negativity and stability analyses of Lattice-Boltzmann Method for advection-diffusion equation, Journal of Computational Physics, 228 (2008), pp. 236-256.
  7. Demuth C., Mendes M.A.A., Ray S., Trimis D. Performance of thermal lattice Boltzmann and finite volume methods for the solution of heat conduction equation in 2D and 3D composite media with inclined and curved interfaces, International Journal of Heat and Mass Transfer, 77 (2014), pp. 979-994.
  8. Perko J., Patel. R. A. Single-relaxation-time lattice Boltzmann scheme for advection-diffusion problems with large diffusion-coefficient heterogeneities and high-advection transport, Physcial Review, 89 (2014), pp. 053309-9, DOI: 10.1103/PhysRevE.89.053309.
  9. Nourgaliev R.R. , Dinh T.N., Theofanous T.G., Joseph D. The lattice Boltzmann equation method: theoretical interpretation, numerics and implications International Journal of Multiphase flow, 29 (2003), 1, pp. 117-169.
  10. Ziegler D.P., Boundary conditions for lattice Boltzmann simulations Journal of Statistical Physics, 71 (1993), 1, pp. 1171-7.
  11. Walther, E., Bennacer, R., De Sa, C., Lattice Boltzmann Method applied to Diffusion in restructured Heterogeneous Media. Defect and Diffusion Forum, 354 (2014), pp. 237-242
  12. E. Roubin, A. Vallade, N. Benkemoun, J.-B. Colliat. Multi-scale failure of heterogeneous materials: a double kinematics enhancement for embedded finite element method International Journal of Solids and Structures, 10 (2014).

© 2017 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence