This paper presents nonlinear iterative methods for the fundamental thermal radiative transfer (TRT) model defined by the time-dependent multifrequency radiative transfer (RT) equation and the material energy balance (MEB) equation. The iterative methods are based on the nonlinear projection approach and use multiple grids in photon frequency. They are formulated by the high-order RT equation on a given grid in photon frequency and low-order moment equations on a hierarchy of frequency grids. The material temperature is evaluated in the subspace of lowest dimensionality from the MEB equation coupled to the effective grey low-order equations. The algorithms apply various multigrid cycles to visit frequency grids. Numerical results are presented to demonstrate convergence of the multigrid iterative algorithms in TRT problems with large number of photon frequency groups.

本文介绍了由瞬态多频辐射传递 (RT) 方程和材料能量平衡 (MEB) 方程定义的基本热辐射传递 (TRT) 模型的非线性迭代方法。迭代方法基于非线性投影方法并在光子频率中使用多个网格。它们由给定光子频率网格上的高阶 RT 方程和频率网格层次结构上的低阶矩方程公式化。材料温度在最低维度的子空间中从 MEB 方程耦合到有效灰度低阶方程进行评估。该算法应用各种多重网格周期来访问频率网格。