A Lattice Boltzmann Scheme for Diffusion Equation in Spherical Coordinate

Debabrata Datta, T K Pal

Abstract


Lattice Boltzmann models for diffusion equation are generally in Cartesian coordinate system. Very few researchers have attempted to solve diffusion equation in spherical coordinate system. In the lattice Boltzmann based diffusion model in spherical coordinate system extra term, which is due to variation of surface area along radial direction, is modeled as source term. In this study diffusion equation in spherical coordinate system is first converted to diffusion equation which is similar to that in Cartesian coordinate system by using proper variable. The diffusion equation is then solved using standard lattice Boltzmann method. The results obtained for the new variable are again converted to the actual variable. The numerical scheme is verified by comparing the results of the simulation study with analytical solution. A good agreement between the two results is established.


Keywords


Radial diffusion; lattice Boltzmann method; spherical coordinate

Full Text:

PDF

References


. Chen S, Doolen GD. Lattice Boltzmann method for fluid flows. Annu. Rev Fluid Mech. 1998; 30: 329-364.

. Succi, S. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford, U. K.: Oxford Univ. Press 2001.

. Wolf-Gladrow, D.A. Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction. New York: Springer 2000.

. Benzi R, Succi S, Vergassola M. The lattice Boltzmann equation: theory and applications, Phys. Rep. 1992; 222: 145-197.

. Frisch U, Hasslacher B, Pomeau Y. Lattice-gas automata for the Navier-Stokes equation, Phys. Rev. Lett. 1986; 56 (14): 1505-1508.

. Guo ZL, Shu C. Lattice Boltzmann method and its application in engineering, World Scientific press 2013.

. Zhao CY, Dai LN, Tang GH, et al. Numerical study of natural convection in porous media (metals) using Lattice Boltzmann Method (LBM), International Journal of Heat and Fluid Flow 2010; 31 (5): 925-934.

. Mohamad A. Lattice Boltzmann Method Fundamentals and Engineering Applications with Computer Codes, Springer, London 2011.

. Zhou JG. Axisymmetric lattice Boltzmann method, Phys. Rev. E 2008; 78: 036701.

. Mohamad AA. Lattice Boltzmann method for heat diffusion in axis-symmetric geometries, Prog. Comput. Fluid Dyn. 2009; 9 (8): 490-494.




DOI: http://dx.doi.org/10.24294/ijmss.v1i4.815

Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Creative Commons License

This site is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.