Radiosity view factor model for sources with general distribution

The radiosity view factor model commonly used in radiation heat transfer and computer graphics is applied to a free-molecular flow problem. This paper extends the model to sources with general distribution and includes the diffuse reflections from surfaces, while the previous model is only compatible with an isotropic source distribution. The derivations of the particle flow rate and density are presented, and the numerical implementation is described. The view factor model is compared to the Monte Carlo particle model for density distributions obtained using two different velocity distribution functions for two sources: (1) a Maxwellian distribution with streaming components in both axial and tangential directions and (2) an arbitrary distribution with a discontinuous feature. In these validation studies, it is shown that the radiosity view factor model predicts the correct density distribution that is much smoother and with less simulation run-time compared to the Monte Carlo particle model. While the model herein is applied to a free-molecular flow problem, it can easily be applied to the other problems with a complex source distribution where intensity as a function of wavelength cannot be integrated analytically.