矩模型的最优预测：Crescendo扩散与重排方程
Optimal prediction for moment models: Crescendo diffusion and reordered equations
AI总结：
针对辐射矩系统的截断封闭问题，研究在最优预测框架下统一推导多种现有封闭方法，提出新型重排$P_N$方程与crescendo扩散改进方案，后者无额外成本且数值近似效果更优。
摘要：
辐射输运方程或任意动理学方程的直接数值求解通常计算成本很高，因为辐射强度依赖于时间、空间和方向。对方向变量进行展开可得到等价的无穷多矩方程组，一个核心问题是如何对该系统进行截断，现有文献已提出多种封闭方法。我们旨在在最优预测（一种用较小系统近似大系统平均解的策略）的框架下，针对辐射矩系统开展矩封闭的一般性研究。我们将该策略应用于辐射输运问题，证明可在此框架下重新推导出多种封闭方法，例如$P_N$、扩散以及扩散校正封闭。此外，该形式体系还衍生出新型抛物型系统——重排$P_N$方程，其形式与简化$P_N$方程相似。我们还对现有封闭方法提出了一种改进方案，新推导的crescendo扩散虽然构造简单且无额外计算成本，但在数值测试中能得到更优的近似结果。
英文摘要：
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent system of infinitely many moments. A fundamental problem is how to truncate the system. Various closures have been presented in the literature. We want to study moment closure generally within the framework of optimal prediction, a strategy to approximate the mean solution of a large system by a smaller system, for radiation moment systems. We apply this strategy to radiative transfer and show that several closures can be re-derived within this framework, e.g. $P_N$, diffusion, and diffusion correction closures. In addition, the formalism gives rise to new parabolic systems, the reordered $P_N$ equations, that are similar to the simplified $P_N$ equations. Furthermore, we propose a modification to existing closures. Although simple and with no extra cost, this newly derived crescendo diffusion yields better approximations in numerical tests.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
