Jo Nov 2, 2023

Radiation is an important process of thermal transfer together with conduction and/or convection. Particularly, in high temperature conditions such as burning of pulverized coal, propellants of rockets and thermal plasma, it contributes significantly to overall thermal transfer. However, due to the integro-differential characteristic of a radiative transfer equation for mathematically explaining thermal radiation in absorbing, emitting and scattering media, its algebraic solution is in existence only for extremely limited geometries and conditions. Thus, numerical methods have mainly been utilized to study radiative thermal transfer. Moreover, the advance on performance of modern computers and the interest increased for understanding thermal radiation have promoted the development of numerical methods to solve the radiative transfer equation at a low cost.

Several numerical methods, such as Monte Carlo method, zonal method, discrete ordinates method, finite element method, etc. were applied to model radiative behavior.

The discrete ordinates method (DOM) is a numerical technique proposed first for analyzing radiative thermal transfer in a slab-parallel medium, which has several advantages: low dimensional approximation with sufficient accuracy, modest computational requirement, and applicability into complex geometry.

There were some attempts to use the lattice Boltzmann method (LBM) as a tool to solve the radiative transfer equation, which has developed into an alternative and promising numerical scheme for simulating fluid flows.

Kim Yong Jun, a researcher at the Faculty of Physics Engineering, has developed a discrete ordinate-lattice Boltzmann method (DO-LBM) by combining the advantages of DOM and LBM that can be utilized as a direct tool to solve the radiative transfer equation.

The discrete ordinates scheme is used for angular discretization and the lattice Boltzmann model is applied for spatial discretization.

Introducing Chapmann-Enskog method and dimensionless numbers, he analyzed accuracy of the DO-LBM and non-negativity of the equilibrium distribution function. He compared his method with numerical results by modified discrete ordinates method. The result showed that analyzing radiative transfer in geometry with complex boundaries lowers computational cost more than modified discrete ordinates method often found in literature.