A Uniform Convergent Method for the Three-Temperature Radiative Transfer Model in Two Different Limits

We present a uniform convergent numerical method for solving the three-temperature radiative transfer model, which holds significant importance in inertial confinement fusion. In several physically meaningful benchmark tests, the mean free path denoted as [Formula: see text] can vary from very small values to [Formula: see text], and the relaxation time of the electron and ion temperatures, [Formula: see text], can span several orders of magnitude, ranging from [Formula: see text] to very large values. A carefully designed splitting method is proposed that can maintain uniform accuracy for all these extreme cases. The proposed scheme captures two important limiting models: the three-temperature radiation diffusion equation (3TRDE) when opacity approaches infinity, i.e., the mean free path [Formula: see text], and the two-temperature limit when the ion-electron coupling coefficient [Formula: see text] goes to infinity. We have demonstrated the uniform convergence and efficiency with respect to these two parameters and the energy conservation characteristics of the proposed scheme, both analytically and numerically. The scheme’s performance has been validated through a series of benchmark tests in the numerical part.