Lattice Boltzmann model combined with immersed boundary method for two-dimensional radiative heat transfer with irregular geometries

A complete lattice Boltzmann model combined with immersed boundary method (LB-IBM) is developed to address radiative heat transfer problem in irregularly shaped media. This method investigates radiative heat transfer in two-dimensional uniform/gradient refractive index media with various geometric shapes. The thermal effects generated by irregular boundaries are represented in the form of thermal density and interpolated onto adjacent lattices in the lattice Boltzmann model (LBM). Then, the four-point discrete delta function is used as the interface scheme of the immersed boundary method. Therefore, the standard LBM can effectively solve radiation problems in irregular geometries. The accuracy of the LB-IBM is validated through a comparative analysis with the results predicted by the finite volume method, embedded boundary method, and other numerical methods. Moreover, this paper promotes the application of LBM in radiative heat transfer in irregularly shaped media by providing a straightforward and efficient mesoscopic tool. This lays the foundation for establishing a framework of LBM for unified treatment of convection, conduction and thermal radiation.