Direct numerical method to solve radiation trapping problems with a Doppler broadening mechanism for partial frequency redistribution

We present a numerical method for solving the Holstein-Biberman-Payne equation with Doppler frequency redistribution. The method is based on direct time propagation of the initial distribution of excited atoms, employing the split-propagation technique. It allows a precise study of various aspects of radiation transfer phenomena occurring in an arbitrary convex three-dimensional spatial region, driven by external conditions with arbitrary time dependencies. We present some results obtained for slab and spherically shaped geometries and compare them to results from other evaluation methods. The efficiency of the method is demonstrated by determining the intensity of radiation escaping the gas cell in afterglow experiments.