An Angular Discretization Method Using Repulsive Particles for the Three-Dimensional Radiative Transfer Equation

In the present study, a new angular discretization method, repulsive particle angular discretization (RPAD), is proposed for use with the three-dimensional radiative transfer equation (RTE). To discretize a solid angle as uniformly as possible, mutually repulsive particles on the unit sphere were introduced and directly used as radiation directions. To assess the uniformity of the radiation direction distributions of the RPAD and the other angular discretization methods, the minimum distances between control angles were compared. The assessment shows that the radiation direction distribution of the RPAD is the most uniform. The RPAD also achieved the most accurate first moment integral over the half solid angle. To assess various angular discretization methods including the RPAD in the three-dimensional spatial domain, they were adopted to solve two benchmark problems. The first benchmark problem is analysis of a cylindrical enclosure fill with a purely absorbing and emitting medium. In this problem, although the maximum radiative flux errors from the FT _n FVM, IUSD, and RPAD were relatively similar, it was observed that the flux by the RPAD exhibits the least fluctuation for the varying surface direction with respect to the coordinate system. As a second benchmark problem, the rocket plume base heating was analyzed to assess the angular discretization methods in terms of pure scattering. It was observed that the maximum errors were smallest for the IUSD or RPAD, followed by the FT _n FVM. However, the IUSD shows a relatively inaccurate radiative flux for a particular number of radiation directions. It was found that the RPAD proposed in the present study provides comparable or more accurate solutions for the three-dimensional RTE than the other angular discretization methods tested.