This work presents efficient solution techniques for radiative transfer in the smoothed particle hydrodynamics discretization. Two choices that impact efficiency are how the material and radiation energy are coupled, which determines the number of iterations needed to converge the emission source, and how the radiation diffusion equation is solved, which must be done in each iteration. The coupled material and radiation energy equations are solved using an inexact Newton iteration scheme based on nonlinear elimination, which reduces the number of Newton iterations needed to converge within each time step. During each Newton iteration, the radiation diffusion equation is solved using Krylov iterative methods with a multigrid preconditioner, which abstracts and optimizes much of the communication when running in parallel. The code is verified for an infinite medium problem, a one-dimensional Marshak wave, and a two and three-dimensional manufactured problem, and exhibits first-order convergence in time and second-order convergence in space. For these problems, the number of iterations needed to converge the inexact Newton scheme and the diffusion equation is independent of the number of spatial points and the number of processors.

这项工作提出了有效的解决方法，用于平滑粒子流体动力学离散化中的辐射传递。影响效率的两个选择是如何耦合材料和辐射能，这决定了收敛发射源所需的迭代次数，以及如何求解辐射扩散方程式，这必须在每次迭代中完成。使用基于非线性消除的不精确牛顿迭代方案求解耦合的材料和辐射能方程，这减少了在每个时间步内收敛所需的牛顿迭代次数。在每个牛顿迭代过程中，使用带有多网格预处理器的Krylov迭代方法求解辐射扩散方程，当并行运行时，该方程抽象并优化了大部分通信。该代码针对无限介质问题，一维Marshak波以及二维和三维制造问题进行了验证，并且在时间上表现出一阶收敛，在空间上表现出二阶收敛。对于这些问题，收敛不精确的牛顿方案和扩散方程所需的迭代次数与空间点的数目和处理器的数目无关。