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We show a numerical scheme to solve the moment equations of the radiativetransfer, i.e., M1 model which follows the evolution of the energy density, $ E$, and the energy flux, $ \mbox{\boldmath$F$} $. In our scheme we reconstructthe intensity from $ E $ and $ \mbox{\boldmath$F$} $ so that it is consistentwith the closure relation, relation, $ \chi = (3 + 4 f ^2)/(5 + 2 \sqrt{4 - 3 f^2}) $.  Here the symbols, $ \chi $, $ f = |\mbox{\boldmath$F$}|/(cE) $, and $ c $,denote the Eddington factor, the reduced flux, and the speed of light,respectively. We evaluate the numerical flux across the cell surface from thekinetically reconstructed intensity. It is an explicit function of $ E $ and $\mbox{\boldmath$F$} $ in the neighboring cells across the surface considered.We include absorption and reemission within a numerical cell in the evaluationof the numerical flux. The numerical flux approaches to the diffusionapproximation when the numerical cell itself is optically thick. Our numericalflux gives a stable solution even when some regions computed are very opticallythick. We show the advantages of the numerical flux with examples. They includeflash of beamed photons and irradiated protoplanetary disks.

Kinetic Scheme for Solving M1 Model of Radiative Transfer