辐射传输过程是一个强非线性、强耦合的过程。为保证计算的稳定性，能量方程的数值离散必须采用全隐格式，且需要采用大量的离散网格单元以保证所需的精度。非线性全隐格式形成的大型非线性代数方程组是病态的，求解的工作量非常巨大。但是，现有的数值方法计算效率较低，且应用中常用的离散格式经常出现的数值越界问题，现有的保界修正算法又往往出现迭代次数明显增加、收敛变慢甚至不收敛的现象，这些方法不能很好地满足实际应用对快速求解的需求。.本项目将开展如下研究：1) 针对现有的单元中心型有限体积格式(包括九点格式和非线性保正格式等)计算效率较低的问题，研究适用于这些格式(包括完全保正格式)的非线性迭代加速方法和Anderson加速算法；2) 研究适用于一般结构网格的有限体积格式(包括保极值原理的离散格式)的几何两网格加速算法；3) 针对现有的保界修正算法收敛慢的问题，将设计新的不影响收敛速度的保界修复算法。

The radiation transmission process is a strongly nonlinear and strongly coupled process. To ensure the stability of the calculation, the numerical discretization of the energy equation must adopt the fully implicit scheme, and there must be a large number of mesh units to ensure the required accuracy. The large system of nonlinear algebraic equations formed by nonlinear fully implicit schemes is ill-conditioned and the workload of solving this system is enormous. However, the existing numerical methods usually have low computational efficiency, and the discreted formula formally used in the practical applications often appear numerical cross-limit problems. The existing correction algorithms often increase the number of iterations, slow convergence or even no convergence, So, these methods can not well meet the practical application demand for rapid solution.. In this project, we propose to consider the following problems: 1) For the low computational efficiency of the cell-centred finite volume method(including nine-point schemes and nonlinear positive preserving schemes), studying the nonlinear iterative acceleration method and the modified Anderson acceleration algorithm for these schemes(including fully positive preserving formula); 2) studying the geometric two-grid acceleration algorithm of finite volume scheme(including preserving maximum principle formula); 3) studying the correction algorithm and how to accelerate the new correcting algorithm without affecting the speed of convergence.