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A Lattice Boltzmann Scheme for Diffusion Equation in Spherical Coordinate
Debabrata Datta
T K Pal
International Journal of Mathematics and Systems Science 2022, 5(1); https://doi.org/10.24294/ijmss.v1i4.815
Submitted:09 May 2018
Accepted:24 May 2018
Published:07 Jun 2022
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.

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