Abstract
In this paper, we develop a maximum principle preserving Monte Carlo method for the frequency-dependent (multi-group) radiative transfer equations. In order to deal with the nonlinear coupling between the radiation intensity and background material, Newton's iteration is involved into the discretization of the nonlinear system. We employ the maximum principle of the material temperature as the stopping criterion of the nonlinear iterations. The classical implicit Monte Carlo method can be regarded as one iteration of the new iterative method. We demonstrate that if the nonlinear iteration of the new method converges, it will become a fully implicit discretization of the multi-group radiative transfer equations. Moreover, the radiation temperature will also satisfy the maximum principle under certain conditions. Several frequency-dependent radiative transfer examples are given to show the effectiveness of the new method.
Published Version
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