A Ghost Fluid Approach for Thermal Lattice Boltzmann Method in Dealing with Heat Flux Boundary Condition in Thermal Problems with Complex Geometries

Abstract

In this paper, the ghost fluid thermal lattice Boltzmann method is improved to properly impose the heat flux boundary condition on complex geometries [Khazaeli, R., S. Mortazavi and M. Ashrafizaadeh (2013). Application of a ghost fluid approach for a thermal lattice Boltzmann method, J. Comput. Phys. 250, 126– 140]. A double-population thermal lattice Boltzmann method is used to handle both the flow and temperature fields on a Cartesian grid and the boundary conditions are imposed using a ghost fluid method. The method is based on the decomposition of the unknown distribution functions into their equilibrium and non-equilibrium parts at every ghost point. The equilibrium parts are determined by performing an extrapolation of major quantities from the image points to the associated ghost points. The bounce-back scheme is then used to determine the non- equilibrium parts. The method benefits from some features such as easy implementation and second order accuracy. The method is applied to simulate natural convection within annuluses with different shapes and boundary conditions,. The obtained results are generally in a good agreement with those predicted by other numerical efforts.

Keywords

• Ghost fluid approach; Thermal lattice Boltzmann method; Fluid flow; Heat transfer; Heat flux boundary condition; Complex geometry.