A direct-forcing IB-LBM implementation for thermal radiation in irregular geometries

Abstract

Radiative heat transfer in two-dimensional irregular geometries is analyzed using a direct-forcing immersed boundary-lattice Boltzmann method (IB-LBM) in participating media. In this paper, the radiative transfer equation (RTE) is discretized by the lattice Boltzmann method, which Yi et al. (Phys Rev E 94(2):023312, 2016) have recently presented. The D2Q9 scheme is used to solve the lattice Boltzmann equation (LBE) and the quadrature scheme SN to discrete the angular space. The irregular geometries’ boundaries are simulated by Immersed Boundary Method (IBM). The effect of boundaries that do not match the computational nodes is determined by adding a radiation density term to the LBE. Radiative heat flux distribution for different extinction coefficients are compared with the results obtained from the blocked-off domain method (BOM), embedded boundary method (EBM), and body-fitted grid method (BFM). Compared to the BFM, the proposed method has perfect accuracy, and for all considered problems, the average percent relative error in the estimation of radiative heat flux is between 0.4 and 9.8%. The results show that IBM can solve the difficulties of simulating curved boundaries efficiently. It is found that IB-LBM has been able to solve the problem of thermal radiation in irregular geometries for media with any optical depth.